Question 1

An equal sum of money is invested in two different schemes for 2 years. One scheme offers simple interest and the other offers compound interest with annual compounding. The rate of interest for both schemes is 23% per annum. If the total interest r…

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Introduction / Context: This question involves comparing simple interest and compound interest on equal principals at the same rate for the same time period. The total interest from both schemes together after 2 years is known, and we must find the first year interest from the simple interest scheme. This requires understanding how simple interest accumulates linearly while compound interest grows by adding interest on interest. Given Data / Assumptions: • Principal P is invested in the simple interest scheme for 2 years at 23% per annum. • The same principal P is invested in the compound interest scheme for 2 years at 23% per annum with annual compounding. • Total interest from both schemes together after 2 years is Rs. 2961. • Simple interest formula: SI = (P * R * T) / 100. • Compound interest amount for 2 years: A = P * (1 + R / 100)^2, CI = A - P. Concept / Approach: We write expressions for the 2-year simple interest and the 2-year compound interest on the same principal P. Adding these expressions and equating the result to Rs. 2961 allows us to solve for P. Once P is known, the first year interest from the simple interest scheme is just P * 23 / 100, since simple interest per year is constant. Step-by-Step Solution: Simple interest for 2 years: SI_2y = P * 23 * 2 / 100 = 0.46P. For compound interest, amount after 2 years: A = P * (1 + 23 / 100)^2 = P * (1.23)^2. Compute (1.23)^2 = 1.5129, so CI_2y = A - P = P * (1.5129 - 1) = 0.5129P. Total interest from both schemes = SI_2y + CI_2y = 0.46P + 0.5129P = 0.9729P. We are given 0.9729P = 2961, so P = 2961 / 0.9729. Using exact fractional reasoning, P = 70000 / 23 ≈ 3043.48. First year interest from simple interest scheme = P * 23 / 100 = (70000 / 23) * 23 / 100 = 70000 / 100 = Rs. 700. Verification / Alternative check: Check total interest with P = 70000 / 23. Simple interest for 2 years = 0.46P = 0.46 * 70000 / 23 = 32200 / 23. Compound interest for 2 years = 0.5129P = 0.5129 * 70000 / 23 = 35980 / 23. Sum = (32200 + 35980) / 23 = 68180 / 23 = 2961. This matches the given total interest, confirming that the first year simple interest of Rs. 700 is correct. Why Other Options Are Wrong: Rs. 500, Rs. 800, Rs. 900, and Rs. 1100 correspond to different assumed principals that do not produce a total interest of Rs. 2961 when both schemes are considered. Substituting these values back into the total interest expression would yield totals significantly different from 2961. Common Pitfalls: A common mistake is to treat compound interest as if it were simple interest and ignore the squaring of the growth factor (1.23)^2. Another error is to attempt separate trial and error for P instead of forming a single equation. Keeping the algebraic structure clear and using exact fractions or careful decimals avoids rounding errors and confusion. Final Answer: The first year interest from the simple interest scheme is Rs. 700.

Question 2

A sum of Rs. 1200 is lent to be repaid in 5 equal annual instalments of Rs. 264 each, where each instalment includes both principal and simple interest. Based on this repayment pattern, what is the annual rate of simple interest per annum?

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Introduction / Context: This question involves a loan that is repaid in equal annual instalments, each instalment including both principal and simple interest. We are given the original principal, the number of instalments, and the instalment amount, and we must determine the annual simple interest rate. The key idea is to recognize that the total of all instalments equals the principal plus the total simple interest over the full term. Given Data / Assumptions: • Principal P = Rs. 1200. • Number of equal annual instalments n = 5. • Each instalment = Rs. 264. • Simple interest is charged at a constant rate R% per annum for 5 years on the original principal. • Total interest I_total = P * R * n / 100 in the simple interest model for this question. Concept / Approach: The sum of the 5 instalments is the total amount repaid. This total equals the original principal plus the simple interest on that principal for the entire 5-year period. We can therefore find the total interest paid, then apply the simple interest formula I_total = (P * R * T) / 100 with T = 5 years to solve for R. Step-by-Step Solution: Total amount repaid over 5 years = 5 * 264 = Rs. 1320. Total interest paid I_total = total repaid - principal = 1320 - 1200 = Rs. 120. Under the simple interest model here, interest for 5 years on P is I_total = (P * R * 5) / 100. So 120 = (1200 * R * 5) / 100. Compute 1200 * 5 / 100 = 60, so equation becomes 120 = 60R. Therefore, R = 120 / 60 = 2% per annum. Verification / Alternative check: At a 2% simple interest rate on Rs. 1200 for 5 years, total interest should be I_total = 1200 * 2 * 5 / 100 = 1200 * 0.1 = Rs. 120, which matches the interest calculated from the instalments. Thus, the repayment schedule of five instalments totalling Rs. 1320 is consistent with a rate of 2% per annum on the original principal. Why Other Options Are Wrong: Rates of 3%, 4%, 5%, or 6% per annum would result in total interest values of 180, 240, 300, and 360 rupees respectively on Rs. 1200 over 5 years. Adding these interest amounts to the principal would yield total repayments different from Rs. 1320, contradicting the instalment information given in the problem. Common Pitfalls: A key pitfall is overcomplicating the problem by attempting to track interest on reducing balances for each year, which is more typical of reducing balance methods. The question, however, treats simple interest on the original principal for the entire period. Misinterpreting the model or forgetting to subtract the principal from the total of instalments before applying the formula can also lead to wrong answers. Final Answer: The annual rate of simple interest is 2% per annum.

Question 3

Alipta receives a certain sum of money from her father and invests it at simple interest at 6% per annum. After some years, the ratio of the original money to the interest earned becomes 10 : 3. In how many years will this ratio 10 : 3 be achieved?

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Introduction / Context: This problem uses a ratio to relate the original principal to the interest earned under simple interest. Alipta invests money at a fixed rate of 6% per annum, and we are told that after some time the ratio of principal to interest becomes 10 : 3. Using this ratio and the simple interest formula, we can determine the number of years required to reach that interest amount. Given Data / Assumptions: • Principal P is some unknown sum received from her father. • Rate of simple interest R = 6% per annum. • After T years, interest I and principal P satisfy P : I = 10 : 3. • Simple interest formula: I = (P * R * T) / 100. Concept / Approach: From the ratio P : I = 10 : 3, we can write P = 10k and I = 3k for some positive constant k. Using the simple interest formula, we substitute I and P in terms of k and solve for T. The principal P cancels out, so we do not need its actual value to find the time. Step-by-Step Solution: Given ratio P : I = 10 : 3, let P = 10k and I = 3k. From simple interest formula: I = (P * R * T) / 100. Substitute P and R: 3k = (10k * 6 * T) / 100. Simplify the right side: (10k * 6 * T) / 100 = (60kT) / 100 = 0.6kT. So 3k = 0.6kT. Divide both sides by k (k ≠ 0): 3 = 0.6T. Therefore, T = 3 / 0.6 = 5 years. Verification / Alternative check: We can pick a convenient value, for example P = Rs. 1000. Then P corresponds to 10 parts, so each part is 100, making I = Rs. 300 when ratio is 10 : 3. At 6% per year, simple interest per year is 6% of 1000 = Rs. 60. To accumulate Rs. 300 interest, time = 300 / 60 = 5 years, confirming our result. Why Other Options Are Wrong: Times of 3, 4, 6, or 7 years would produce interest values that correspond to different ratios than 10 : 3. For example, at 6% per year on Rs. 1000, 3 years gives Rs. 180 interest (ratio 1000 : 180 = 50 : 9), not 10 : 3. Similar mismatches occur for 4, 6, and 7 years. Common Pitfalls: Some students mistakenly interpret the ratio as interest to principal instead of principal to interest, which inverts the relationship. Others forget that P cancels when using the ratio, and they attempt to assume awkward principal values. Working systematically with proportional expressions keeps the algebra simple. Final Answer: The required time is 5 years.

Question 4

If a sum of money becomes double of itself in 8 years at simple interest, what is the rate of interest per annum, expressed as a percentage?

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Introduction / Context: This is a classic simple interest question about the time taken for a sum to double and the corresponding interest rate. Under simple interest, the amount increases linearly with time, so once we know that a sum doubles in a certain number of years, we can directly determine the annual rate of interest that produces this doubling. Given Data / Assumptions: • Principal (original sum) is P. • Amount after 8 years is 2P, meaning the sum doubles in 8 years. • Time T = 8 years. • Rate of simple interest is R% per annum to be found. • Simple interest formula: A = P * (1 + R * T / 100). Concept / Approach: Since A = 2P after 8 years, the total interest over those 8 years is P. Using the simple interest amount formula and equating it to 2P, we can solve for R. This uses the fact that, under simple interest, the extra amount over principal is proportional to time and rate: P * R * T / 100 = interest. Step-by-Step Solution: Given that amount after 8 years is A = 2P. Simple interest amount formula: A = P * (1 + R * T / 100). Substitute T = 8: 2P = P * (1 + 8R / 100). Divide both sides by P (P ≠ 0): 2 = 1 + 8R / 100. So 8R / 100 = 1, giving 8R = 100. Therefore, R = 100 / 8 = 12.5% per annum. Verification / Alternative check: If P = Rs. 100 for simplicity, then at 12.5% per annum simple interest, yearly interest is Rs. 12.50. Over 8 years, total interest = 8 * 12.50 = Rs. 100. The final amount after 8 years is 100 + 100 = Rs. 200, which is exactly double the original Rs. 100, confirming that 12.5% is correct. Why Other Options Are Wrong: Rates of 8.5%, 10%, 10.5%, and 14% produce different total interest over 8 years. For example, at 10%, total interest in 8 years is 80% of P, giving a final amount of 1.8P, which is less than double. At 14%, total interest is 112% of P, which overshoots the doubling condition. Common Pitfalls: Some learners confuse simple interest with compound interest and try to use doubling rules from compound interest. Others incorrectly divide 8 by 2 or use half of 8 in the formula. The correct method is to write out the simple interest amount expression, substitute A = 2P, and solve linearly for R. Final Answer: The rate of interest per annum is 12.5%.

Question 5

Simple Interest vs Compound Interest: On a certain principal, the simple interest (SI) for 2 years is ₹4,000 and the compound interest (CI) for the same 2 years at the same annual rate is ₹4,180. What is the rate of interest per annum (in %)?

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Introduction / Context: This question compares simple interest (SI) and compound interest (CI) on the same principal over the same time period and asks you to determine the annual rate of interest. Such questions are common in bank exams and aptitude tests and help you understand how compounding increases the interest earned compared with simple interest. Given Data / Assumptions: Principal = P (same for SI and CI). Time = 2 years. Simple interest for 2 years = ₹4,000. Compound interest for 2 years = ₹4,180. Rate of interest per annum = r% (same for SI and CI). Interest is compounded annually for CI. Concept / Approach: For simple interest, SI = (P * r * t) / 100. For compound interest with annual compounding for 2 years, CI = P * ((1 + r / 100)^2 - 1). Because SI and CI are both given, we can first find the product P * r from the SI expression and then substitute into the CI expression to test which rate from the options satisfies both conditions. Step-by-Step Solution: Step 1: Using simple interest: SI for 2 years = (P * r * 2) / 100 = ₹4,000. Step 2: Rearranging, P * r = (4,000 * 100) / 2 = 200,000. Step 3: For compound interest for 2 years: CI = P * ((1 + r / 100)^2 - 1) = ₹4,180. Step 4: Test the given options for r (in %): 6, 12, 9, 7.5, 4.5. Step 5: Try r = 9%. Then P = 200,000 / 9 ≈ 22,222.22. Step 6: Compute CI for r = 9%: CI = 22,222.22 * ((1.09^2) - 1) = 22,222.22 * (1.1881 - 1) = 22,222.22 * 0.1881 ≈ ₹4,180. Step 7: The result exactly matches the given CI = ₹4,180, so r = 9% satisfies both conditions. Step 8: Therefore, the required rate of interest is 9% per annum. Verification / Alternative check: Once you have r = 9%, you can quickly verify SI: SI = (P * r * 2) / 100 = (22,222.22 * 9 * 2) / 100 ≈ ₹4,000. This confirms that both the SI and CI values are consistent with r = 9% per annum, so no other option is needed. Why Other Options Are Wrong: 6%: At this rate, the CI for 2 years is too small (around ₹4,120) and does not match ₹4,180. 12%: At 12%, the 2 year CI is about ₹4,240, which is greater than ₹4,180. 7.5%: At 7.5%, CI is about ₹4,150, still not equal to ₹4,180. 4.5%: At 4.5%, CI is about ₹4,090, clearly less than ₹4,180. Common Pitfalls: Students often try to apply a shortcut based only on the difference between CI and SI without writing the equations. Another mistake is to forget that SI for 2 years is proportional to 2r, whereas CI depends on (1 + r / 100)^2. Always form the correct equations for SI and CI and then test the options logically. Final Answer: The correct annual rate of interest is 9% per annum.

Question 6

Simple and Compound Interest Comparison: In 2 years at simple interest, a principal amount increases by 8% in total. At the same annual rate, compounded annually, what will be the compound interest (in ₹) earned on ₹10,00,000 in 2 years?

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Introduction / Context: This problem links simple interest (SI) information with compound interest (CI) at the same rate. You are told how much a principal grows over 2 years under simple interest and then asked to find the compound interest on a specific principal over the same period and rate. This is a classic aptitude question that checks whether you can switch between SI and CI correctly. Given Data / Assumptions: Under simple interest, a principal increases by 8% in 2 years. Principal for the CI calculation = ₹10,00,000. Time for CI = 2 years. Compounding is annual. Rate of interest is the same in both cases. Concept / Approach: If a sum increases by 8% in 2 years under simple interest, that means the total SI in 2 years is 8% of the principal. For SI, SI = (P * r * t) / 100, so over 2 years the effective increase is 2r%. Therefore, 2r = 8, giving r = 4% per annum. Once we know r, we can compute CI on ₹10,00,000 using the compound interest formula with annual compounding for 2 years: Amount A = P * (1 + r / 100)^2, CI = A - P. Step-by-Step Solution: Step 1: From SI information, total increase in 2 years = 8% of the principal. Step 2: Under SI, effective 2 year increase = 2r%. So 2r = 8. Step 3: Solve for r: r = 8 / 2 = 4% per annum. Step 4: For CI, principal P = ₹10,00,000 and time t = 2 years at r = 4% compounded annually. Step 5: Compute amount A: A = P * (1 + r / 100)^2 = 10,00,000 * (1.04)^2. Step 6: (1.04)^2 = 1.0816, so A = 10,00,000 * 1.0816 = ₹10,81,600. Step 7: Compound interest CI = A - P = 10,81,600 - 10,00,000 = ₹81,600. Step 8: Therefore, the CI earned is ₹81,600. Verification / Alternative check: You can verify quickly by observing that for 4% per annum, SI for 2 years would be 8% of ₹10,00,000, that is ₹80,000. CI must be slightly greater than SI because interest also earns interest in the second year. The computed CI of ₹81,600 is just a bit more than ₹80,000, which is logically consistent. Why Other Options Are Wrong: ₹90,000: This is too high and would require a rate higher than 4%. ₹86,000: Also larger than the correct CI, not matching 4% compounded for 2 years. ₹94,000: Much too high for only 4% per annum over 2 years. ₹80,000: This equals the 2 year simple interest, not the compound interest, so it ignores compounding. Common Pitfalls: Many learners mistakenly treat the 8% increase as an annual rate instead of the 2 year increase, which would give r = 8% instead of 4%. Others compute simple interest again instead of using the compound interest formula. Always interpret the time period carefully and choose the correct formula (SI or CI) for the quantity being asked. Final Answer: The compound interest on ₹10,00,000 for 2 years at the same rate is ₹81,600.

Question 7

Simple and Compound Interest on the Same Sum: The simple interest (SI) on a certain sum for 3 years is ₹6,000, and the compound interest (CI) on the same sum for 2 years at the same annual rate (compounded annually) is ₹4,160. What is the annual rat…

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Introduction / Context: This question combines information about simple interest (SI) over 3 years and compound interest (CI) over 2 years on the same principal and at the same rate. You are required to find the common annual rate of interest. Such mixed SI and CI problems are popular in aptitude exams as they test your ability to use formulas and relate different time periods. Given Data / Assumptions: Principal = P. Time for SI = 3 years. Simple interest for 3 years = ₹6,000. Time for CI = 2 years. Compound interest for 2 years (annual compounding) = ₹4,160. Rate of interest per annum = r% (same for both SI and CI). Concept / Approach: For SI: SI = (P * r * t) / 100. From the SI data, we can find the product P * r. For CI with annual compounding: CI = P * ((1 + r / 100)^2 - 1) over 2 years. Once P * r is known, we can test the given options for r, compute the corresponding principal P, and then verify which r makes the CI equal to ₹4,160. Step-by-Step Solution: Step 1: From SI, we have SI for 3 years = ₹6,000. Step 2: Use the SI formula: 6,000 = (P * r * 3) / 100. Step 3: Rearranging, P * r = (6,000 * 100) / 3 = 200,000. Step 4: For CI over 2 years, CI = P * ((1 + r / 100)^2 - 1) = ₹4,160. Step 5: Test r = 8% (a likely mid value). Then P = 200,000 / 8 = ₹25,000. Step 6: Compute CI with P = 25,000 and r = 8%: Amount A = 25,000 * (1.08)^2 = 25,000 * 1.1664 = ₹29,160. Step 7: CI = A - P = 29,160 - 25,000 = ₹4,160, which matches the given CI. Step 8: Therefore, the annual rate of interest is 8% per annum. Verification / Alternative check: To confirm, you can compute SI for 3 years at 8% per annum on ₹25,000: SI = (25,000 * 8 * 3) / 100 = 25,000 * 0.24 = ₹6,000, which matches the given SI. Both SI and CI conditions are satisfied simultaneously, so r = 8% is definitely correct. Why Other Options Are Wrong: 9%: Leads to a different principal and CI around ₹4,180, not ₹4,160. 6%: Produces a CI of about ₹4,120 for 2 years, smaller than required. 10%: Gives a CI of around ₹4,200, larger than the given CI. 12%: Produces an even higher CI, far from ₹4,160. Common Pitfalls: Students sometimes directly equate SI and CI or confuse the time durations. Others forget that SI depends linearly on time (3 years) while CI has a squared factor for 2 years. The safest method is to first compute P * r from SI, then systematically test the provided rate options in the CI formula until you match the given CI. Final Answer: The required annual rate of interest is 8% per annum.

Question 8

Comparing Simple Interest in the Third Year with Compound Interest: On a certain principal, the simple interest earned in the 3rd year alone is ₹1,750 (so the yearly simple interest is constant). If the compound interest on the same sum for 2 years …

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Introduction / Context: This question links the simple interest earned in a single year (the 3rd year) with the total compound interest for 2 years on the same principal at the same rate. It tests your understanding that in simple interest the yearly interest is constant, while compound interest grows because interest itself earns interest. Given Data / Assumptions: Principal = P. Simple interest in the 3rd year alone = ₹1,750. This implies yearly SI is constant at ₹1,750. Compound interest for 2 years at the same rate (annual compounding) = ₹3,622.5. Rate of interest per annum = r% (same for both SI and CI). Concept / Approach: For simple interest, interest per year is P * r / 100 and is the same in every year. So the 3rd year SI equals P * r / 100. For compound interest with annual compounding for 2 years, CI = P * ((1 + r / 100)^2 - 1). From the first relation, we can express P in terms of r and the known yearly SI of ₹1,750. Then we substitute this P into the CI formula and test option values of r until the computed CI equals ₹3,622.5. Step-by-Step Solution: Step 1: From SI, yearly interest = P * r / 100 = ₹1,750. Step 2: Rearranging, P = (1,750 * 100) / r. Step 3: For CI over 2 years: CI = P * ((1 + r / 100)^2 - 1) = ₹3,622.5. Step 4: Substitute P into the CI formula and test the options for r. Step 5: Try r = 7%. Then P = (1,750 * 100) / 7 = ₹25,000. Step 6: Compute CI at r = 7%: A = 25,000 * (1.07)^2 = 25,000 * 1.1449 = ₹28,622.5. Step 7: CI = A - P = 28,622.5 - 25,000 = ₹3,622.5, which exactly matches the given CI. Step 8: Therefore, the annual rate of interest is 7% per annum. Verification / Alternative check: With r = 7% and P = ₹25,000, the yearly SI is (25,000 * 7) / 100 = ₹1,750, confirming the 3rd year simple interest. The calculated CI for 2 years also matches the given ₹3,622.5. Since both conditions are satisfied for r = 7% and no other option will satisfy both simultaneously, the answer is confirmed. Why Other Options Are Wrong: 8%: Gives a different principal and CI around ₹3,640, not ₹3,622.5. 9%: Produces CI that is larger than required, around ₹3,657.5. 10%: Leads to an even higher CI, not matching the given value. 6%: Results in CI around ₹3,605, which is too low. Common Pitfalls: Some students mistakenly treat the 3rd year simple interest as 3 times the annual interest or mix up SI and CI formulas. Remember that in simple interest, yearly interest is constant, so the 3rd year SI is exactly equal to the yearly SI. Always set up the equations carefully before substituting values from the options. Final Answer: The correct annual rate of interest is 7% per annum.

Question 9

Simple Interest vs Compound Interest on Different Sums: The simple interest on a certain sum for 3 years at 14% per annum is equal to half of the compound interest on ₹10,000 for 2 years at 10% per annum (compounded annually). What is the sum (princ…

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Introduction / Context: This question compares simple interest (SI) on one sum with compound interest (CI) on another sum. You are told that the SI for 3 years at 14% per annum equals half of the CI on ₹10,000 for 2 years at 10% per annum. The aim is to find the principal on which the simple interest was calculated. This is a standard aptitude problem on the relationship between SI and CI. Given Data / Assumptions: Principal for SI = P (unknown). Time for SI = 3 years. SI rate = 14% per annum. Principal for CI = ₹10,000. CI rate = 10% per annum, compounded annually. Time for CI = 2 years. SI for 3 years = half of CI on ₹10,000 for 2 years. Concept / Approach: First, compute the compound interest on ₹10,000 at 10% per annum for 2 years. Then divide that CI value by 2 to obtain the simple interest earned on the unknown principal P. Next, use the SI formula SI = (P * r * t) / 100 with r = 14% and t = 3 years to solve for P. This algebraic approach is straightforward and avoids unnecessary trial and error. Step-by-Step Solution: Step 1: Compute the CI on ₹10,000 at 10% per annum for 2 years. Step 2: Amount A = 10,000 * (1 + 10 / 100)^2 = 10,000 * (1.1)^2 = 10,000 * 1.21 = ₹12,100. Step 3: CI = A - P = 12,100 - 10,000 = ₹2,100. Step 4: Given that the SI on P for 3 years at 14% equals half of this CI, SI = 2,100 / 2 = ₹1,050. Step 5: Use SI formula: 1,050 = (P * 14 * 3) / 100. Step 6: Simplify: 1,050 = (42P) / 100, so 1,050 * 100 = 42P. Step 7: P = (1,050 * 100) / 42 = 105,000 / 42 = ₹2,500. Step 8: Therefore, the required principal is ₹2,500. Verification / Alternative check: Check SI on ₹2,500 at 14% per annum for 3 years: SI = (2,500 * 14 * 3) / 100 = 2,500 * 0.42 = ₹1,050. Half of the CI on ₹10,000 for 2 years at 10% was found to be ₹1,050, so the condition is satisfied exactly. This confirms that the principal is correct. Why Other Options Are Wrong: ₹5,000: SI for 3 years at 14% would be ₹2,100, which equals the full CI, not half of it. ₹2,000: SI would be ₹840, which is less than half of the given CI. ₹1,250: SI would be ₹525, far too small. ₹3,000: SI would be ₹1,260, larger than the required ₹1,050. Common Pitfalls: A common mistake is to misinterpret the phrase “half of the compound interest” and incorrectly relate SI directly to the amount instead of the CI. Another error is to mix up the principals or rates for SI and CI. Always compute CI on the given sum first, then apply the given relationship to find SI and, finally, use the SI formula to determine the unknown principal. Final Answer: The sum placed at simple interest is ₹2,500.

Question 10

Finding the Simple Annual Interest Rate: You deposit $600 into a certificate of deposit (CD) for 6 months, and after 6 months the balance becomes $618. Assuming simple interest, what is the simple annual interest rate (in % per annum)?

Accepted Answer

Introduction / Context: This problem is a straightforward application of the simple interest formula. You know the initial deposit, the final balance after a certain time, and the time period. From this, you must determine the annual rate of simple interest. Such questions are very common in introductory finance and aptitude tests. Given Data / Assumptions: Principal P = $600. Final balance after 6 months = $618. Time t = 6 months = 0.5 years. Interest earned I = final balance − principal = 618 − 600 = $18. Assume simple interest and a constant annual rate r%. Concept / Approach: The simple interest formula is I = (P * r * t) / 100, where I is interest, P is principal, r is the annual rate in percent, and t is time in years. Here, I, P, and t are known, so we can rearrange the formula to solve for r. This is a direct one step algebra problem once you identify the correct formula and convert months into years. Step-by-Step Solution: Step 1: Compute the interest earned: I = 618 − 600 = $18. Step 2: Convert the time into years: t = 6 months = 6 / 12 = 0.5 years. Step 3: Use the SI formula: I = (P * r * t) / 100. Step 4: Substitute known values: 18 = (600 * r * 0.5) / 100. Step 5: Simplify the right side: (600 * 0.5) / 100 = 300 / 100 = 3. Step 6: So 18 = 3 * r, which gives r = 18 / 3 = 6. Step 7: Therefore, the simple annual interest rate is 6% per annum. Verification / Alternative check: At 6% per annum, the yearly interest on $600 is (600 * 6) / 100 = $36. For half a year (0.5 years), simple interest would be 36 * 0.5 = $18, giving a final balance of 600 + 18 = $618, which matches the problem statement. This confirms the correctness of r = 6%. Why Other Options Are Wrong: 5%: Yearly interest would be $30, so for 6 months it would be $15, giving a final balance of $615, not $618. 7%: Half year interest would be $21, leading to $621, which is too high. 8%: Half year interest would be $24, giving $624. 4%: Half year interest would be $12, giving only $612. Common Pitfalls: Students sometimes forget to convert months into years and incorrectly use t = 6 instead of t = 0.5. Another common mistake is to treat the $18 as the annual interest, which would underestimate the rate. Always express time in years when using the basic simple interest formula. Final Answer: The simple annual interest rate is 6% per annum.

Question 11

Data Sufficiency – Finding Principal from Simple Interest: What is the principal sum (in ₹) that earned the interest? Statement I: The total simple interest is ₹7,000 after 7 years. Statement II: The total of principal and simple interest becomes do…

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Introduction / Context: This is a data sufficiency question on simple interest. Instead of asking you to compute a numerical value directly, it asks whether the given statements provide enough information to determine the principal. You must analyse each statement independently and then together, using the simple interest formula, without necessarily computing the final numeric principal. Given Data / Assumptions: We are dealing with simple interest at some annual rate r%. Principal = P (unknown). Statement I: Total simple interest is ₹7,000 after 7 years. Statement II: Amount (principal + interest) becomes double of the principal after 5 years at the same rate. The rate r is constant over time. Concept / Approach: For simple interest, I = (P * r * t) / 100, where I is interest, P is principal, r is rate, and t is time in years. Data sufficiency problems require deciding whether a statement or combination of statements is enough to uniquely determine P. We are not required to calculate P explicitly, but we can do it to verify understanding. Step-by-Step Solution: Step 1: Analyse Statement I alone. It gives I = 7,000 for t = 7 years, so 7,000 = (P * r * 7) / 100. Step 2: Rearranging, P * r = (7,000 * 100) / 7 = 100,000. This relation involves two unknowns P and r, so P cannot be uniquely found. Step 3: Therefore, Statement I alone is not sufficient. Step 4: Analyse Statement II alone. The amount doubles in 5 years, so P + I = 2P, hence I = P. Step 5: Under SI, I for 5 years is (P * r * 5) / 100, so (P * r * 5) / 100 = P, giving r = 100 / 5 = 20%. Step 6: Statement II alone gives r = 20% but no information about the actual value of P, so P is still unknown. Step 7: Combine Statements I and II. From I: P * r = 100,000. From II: r = 20%. So P = 100,000 / 20 = ₹5,000. Step 8: Only by using both statements together do we get a unique principal P. Verification / Alternative check: With P = ₹5,000 and r = 20%, SI for 7 years would be (5,000 * 20 * 7) / 100 = 5,000 * 1.4 = ₹7,000, matching Statement I. Amount after 5 years would be P + I = 5,000 + (5,000 * 20 * 5) / 100 = 5,000 + 5,000 = ₹10,000, which is double the principal, matching Statement II. Thus both statements are consistent and jointly sufficient. Why Other Options Are Wrong: Statement I alone is sufficient: Incorrect, because it leaves two unknowns (P and r) in one equation. Statement II alone is sufficient: Incorrect, as it only determines r, not P. Either statement alone is sufficient: Incorrect for the reasons above. Both statements not sufficient: Incorrect, because together they clearly determine P. Common Pitfalls: Many test takers mistakenly stop when they find r from Statement II and assume this is enough to answer the question, forgetting that the question asks for the principal. Others try to compute P from Statement I alone and ignore that r is unknown. In data sufficiency, always check whether the variables of interest can be uniquely determined from the information provided. Final Answer: The correct choice is Both Statement I and Statement II are necessary to determine the principal.

Question 12

Finding Simple Interest for a Fractional Rate and Time: What is the simple interest (SI) on ₹68,000 at 16 2/3% per annum for 9 months, assuming simple interest and that 16 2/3% is first converted into a usable fraction or decimal?

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Introduction / Context: This question involves a fractional rate of interest (16 2/3%) and a time period of less than one year (9 months). You must correctly convert both the mixed number percentage and the months into suitable forms and then apply the simple interest formula. This tests attention to detail in handling fractions and time conversions. Given Data / Assumptions: Principal P = ₹68,000. Rate r = 16 2/3% per annum. Time t = 9 months. Simple interest is used. Concept / Approach: First, convert the mixed percentage 16 2/3% into an improper fraction or decimal. Then convert 9 months into years because the simple interest formula uses years. Finally, apply SI = (P * r * t) / 100. Working carefully with fractions helps avoid calculator mistakes and improves understanding of proportional reasoning in interest calculations. Step-by-Step Solution: Step 1: Convert 16 2/3% to an improper fraction. 16 2/3 = (50 / 3)%. Step 2: In decimal form, (50 / 3)% ≈ 16.6667%, but we will keep it as 50 / 3 for cleaner algebra. Step 3: Convert 9 months to years: t = 9 / 12 = 3 / 4 years. Step 4: Use the SI formula: SI = (P * r * t) / 100. Step 5: Substitute values: SI = (68,000 * (50 / 3) * (3 / 4)) / 100. Step 6: Simplify: (50 / 3) * (3 / 4) = 50 / 4 = 12.5. Step 7: So SI = (68,000 * 12.5) / 100 = 68,000 * 0.125 = ₹8,500. Step 8: Therefore, the simple interest is ₹8,500. Verification / Alternative check: Note that 16 2/3% per year is 1 / 6 of the principal per year, since (16 2/3) / 100 = 1 / 6. For 9 months, which is 3 / 4 of a year, the interest is P * (1 / 6) * (3 / 4) = P / 8. Here, P / 8 = 68,000 / 8 = ₹8,500, confirming the previous calculation. Why Other Options Are Wrong: ₹7,500 and ₹8,000: Both are less than P / 8 and correspond to using incorrect fractions or time conversions. ₹9,500: Larger than P / 8, indicating an overestimation of either the rate or time. ₹6,500: Far too low and not equal to P / 8. Common Pitfalls: Many candidates misconvert 16 2/3% as 16.23% or 16.33% instead of 16.6667%. Others forget to convert 9 months to years and use t = 9, which greatly inflates the interest. Always express mixed fractions correctly and convert months into years when using standard interest formulas. Final Answer: The simple interest on ₹68,000 is ₹8,500.

Question 13

Data Sufficiency – Simple Interest Rate on a Loan: At what simple interest rate per annum (in %) did Anand pay interest to Deepak? Statement I: Anand borrowed ₹8,000 from Deepak for 4 years. Statement II: Anand returned ₹8,800 to Deepak at the end o…

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Introduction / Context: This is another data sufficiency question involving simple interest. You must decide whether the given statements provide enough information to determine the simple interest rate at which Anand paid interest to Deepak. The focus is on logical sufficiency, not just computation, so you must analyse each statement separately and then together. Given Data / Assumptions: Simple interest is charged at a constant annual rate r%. Principal borrowed from Deepak = P. Statement I: P = ₹8,000 and the intended loan duration mentioned is 4 years. Statement II: Anand repaid ₹8,800 after 2 years and closed the loan. Interest is simple, not compound. Concept / Approach: Under simple interest, I = (P * r * t) / 100. To find r, we need P, I, and t. Data sufficiency questions ask whether these pieces of information can be uniquely determined. Statement I gives P and a time period but no information about the actual interest paid. Statement II gives a repayment amount and time but does not explicitly state P. Only by combining them do we know both P and the amount repaid after a known time. Step-by-Step Solution: Step 1: Consider Statement I alone. It says Anand borrowed ₹8,000 for 4 years. Step 2: Without knowing how much he repaid or what interest was charged, we cannot find the rate r from Statement I alone. Step 3: Therefore, Statement I alone is not sufficient. Step 4: Consider Statement II alone. It tells us that Anand repaid ₹8,800 after 2 years, settling the loan. Step 5: Statement II does not explicitly tell us what the original principal P was; we only know the total repayment and time, not how much of this is principal versus interest. Step 6: Without knowing P, we cannot find r from Statement II alone, since many combinations of P and r could give the same total of ₹8,800 after 2 years. Step 7: Combine Statements I and II. From I, P = ₹8,000. Step 8: From II, total repayment after 2 years is ₹8,800, so interest I over 2 years = 8,800 − 8,000 = ₹800. Step 9: Apply SI formula: I = (P * r * t) / 100 ⇒ 800 = (8,000 * r * 2) / 100. Step 10: Simplify: 800 = 160r, so r = 800 / 160 = 5% per annum. Verification / Alternative check: Check with r = 5% per annum, P = ₹8,000, and t = 2 years. SI = (8,000 * 5 * 2) / 100 = 800. Amount = 8,000 + 800 = ₹8,800, which matches Statement II. The 4 year mention in Statement I is not used directly in the calculation but still appears as part of the loan description; what matters is that both statements are needed to fix P and I over a specific period. Why Other Options Are Wrong: Statement I alone is sufficient: Incorrect, because interest or repayment is not provided. Statement II alone is sufficient: Incorrect, because original principal is not given. Either statement alone is sufficient: Incorrect, since neither alone is enough. Both statements not sufficient: Incorrect, as combining them allows us to calculate r uniquely. Common Pitfalls: Some students incorrectly assume Statement II implies that ₹8,800 is entirely interest or misread the time periods. Others ignore the need to know both principal and interest to find the rate. In data sufficiency, always identify how many independent equations you have and whether they are enough to determine the required variable uniquely. Final Answer: The correct choice is Both Statement I and Statement II are necessary to determine the rate of interest.

Question 14

Data Sufficiency – Finding the Simple Interest Rate: What is the rate of simple interest per annum (in %)? Statement I: The total interest earned was ₹4,000. Statement II: The sum was invested for 4 years. Assume simple interest and that no other in…

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Introduction / Context: This data sufficiency question tests whether you can determine the simple interest rate when given limited information. You must decide if knowing the total interest or the time period, separately or together, is enough to determine the annual rate of interest. The key is to understand how many variables must be known in the simple interest formula. Given Data / Assumptions: Simple interest is used. Principal = P (unknown). Rate per annum = r% (unknown). Time = t years. Statement I: Total interest earned I = ₹4,000. Statement II: Time t = 4 years. Concept / Approach: The simple interest formula is I = (P * r * t) / 100. There are three key variables P, r, and t, plus the interest I. To find r, we need enough independent equations to eliminate the other unknowns. Data sufficiency problems focus on whether the given statements provide enough equations, rather than on doing calculations. Step-by-Step Solution: Step 1: Analyse Statement I alone. It gives I = ₹4,000 but says nothing about P, r, or t. Step 2: With only I known and three other unknowns, we cannot determine r. Hence, Statement I alone is not sufficient. Step 3: Analyse Statement II alone. It gives t = 4 years. Step 4: Without knowing P, r, or I, Statement II alone is clearly not sufficient to determine r. Step 5: Combine Statements I and II. We now know I = 4,000 and t = 4 years, but P and r are still both unknown. Step 6: The SI formula becomes 4,000 = (P * r * 4) / 100, or P * r = 100,000. Step 7: This is a single equation in two unknowns (P and r), so r cannot be uniquely determined because many combinations of P and r satisfy P * r = 100,000. Step 8: Therefore, even together, Statements I and II are not sufficient to find the rate. Verification / Alternative check: To see why r is not unique, suppose r = 10%. Then P must be 10,000 to make P * r = 100,000. If r = 20%, P must be 5,000. Using both pairs, you still get I = 4,000 over 4 years, but the rate is different in each case. Hence, the information is insufficient to determine a unique r. Why Other Options Are Wrong: Statement I alone is sufficient: Incorrect, as it does not give P, r, or t individually. Statement II alone is sufficient: Incorrect, as knowing only time cannot give the rate. Either statement alone is sufficient: Incorrect because neither alone works. Both statements are necessary: Even together they are not enough, so this is wrong. Common Pitfalls: Many learners see I = 4,000 and t = 4 and mistakenly assume they can find r, forgetting that P is unknown. In data sufficiency, you must always check how many unknowns remain after combining all statements. If more than one unknown remains and only one equation is available, the data is not sufficient. Final Answer: The correct choice is Both Statement I and Statement II are not sufficient to determine the rate of interest.

Question 15

Simple Interest with Minimum Monthly Balance: At the beginning of March, Ryan has $621 in his savings account and on 10 March he deposits an additional $60. The bank pays 8% per annum simple interest, credited monthly, and calculates interest on the…

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Introduction / Context: This question shows how some banks calculate interest on savings accounts using simple interest and the minimum monthly balance method. The interest is credited monthly, but the rate is annual. You must identify the minimum balance during the month and then compute one month's simple interest on that amount. Given Data / Assumptions: Initial balance on 1 March = $621. Additional deposit on 10 March = $60, so balance becomes $681 after that date. Annual simple interest rate r = 8% per annum. Interest is calculated on the minimum monthly balance. Interest is credited monthly, i.e., for one month at a time. Concept / Approach: Under the minimum monthly balance method, the bank pays interest on the lowest balance in that month, regardless of later deposits that may raise the balance. Because Ryan starts with $621 and later adds $60 (raising the balance), the minimum balance is $621. Monthly interest is computed using simple interest for t = 1 / 12 year on this minimum balance at the annual rate of 8%. Step-by-Step Solution: Step 1: Identify the minimum balance for March. From 1 March until 9 March, balance is $621. From 10 March onwards, balance is $681. Step 2: The minimum balance during the month is therefore $621. Step 3: Annual simple interest rate r = 8% per annum. Step 4: Time for one month t = 1 / 12 year. Step 5: Use SI formula I = (P * r * t) / 100 with P = 621. Step 6: I = (621 * 8 * (1 / 12)) / 100 = (621 * 8) / (12 * 100). Step 7: First compute 621 * 8 = 4,968. Step 8: Now divide by 12 * 100 = 1,200: I = 4,968 / 1,200 ≈ $4.14. Step 9: Therefore, Ryan earns approximately $4.14 interest for March. Verification / Alternative check: You can think of the annual interest on $621 at 8% as (621 * 8) / 100 = $49.68. For one month, that is roughly 49.68 / 12 ≈ $4.14. This matches the earlier calculation and confirms that the answer is consistent. Why Other Options Are Wrong: $2.14 and $3.14: Both are too small and would correspond to a lower annual rate or a shorter time period. $5.14: Slightly larger than the correct value and does not match 8% per annum for one month. $4.80: Corresponds to a higher effective rate or a larger minimum balance than $621. Common Pitfalls: Students often mistakenly calculate interest on the highest balance ($681) instead of the minimum balance. Others forget to convert the annual rate to a monthly period and directly use 8% as if it were the monthly rate. Always read the bank's interest calculation rule carefully and adjust the time and balance accordingly. Final Answer: The interest Ryan earns for March is $4.14.

Question 16

Simple Interest on Debentures Paid Quarterly: Jaclyn buys $50,000 worth of debentures that earn 9.5% per annum simple interest, paid quarterly (every 3 months). If the debenture term is 18 months, what is the total simple interest earned over the fu…

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Introduction / Context: This problem asks you to compute simple interest on debentures where interest is paid quarterly. Although payments are quarterly, the underlying rate is annual and the interest is still simple, not compound. The key is to convert the total term into years and then apply the simple interest formula to find the total interest over the entire period. Given Data / Assumptions: Principal P = $50,000. Annual simple interest rate r = 9.5% per annum. Interest is paid quarterly, but interest is simple (no compounding). Term of the debentures = 18 months. Concept / Approach: Under simple interest, the timing of payments (monthly, quarterly, or annually) does not affect the total interest; what matters is the total time in years, principal, and rate. We convert 18 months into years, then use I = (P * r * t) / 100. The quarterly payments simply mean this total interest will be split into 6 equal payments, but the total accumulated interest is what the question asks for. Step-by-Step Solution: Step 1: Convert the term into years: 18 months = 18 / 12 = 1.5 years. Step 2: Use the simple interest formula I = (P * r * t) / 100. Step 3: Substitute P = 50,000, r = 9.5, and t = 1.5. Step 4: I = (50,000 * 9.5 * 1.5) / 100. Step 5: First compute 9.5 * 1.5 = 14.25. Step 6: Then I = (50,000 * 14.25) / 100 = 50,000 * 0.1425. Step 7: Multiply: 50,000 * 0.1425 = $7,125. Step 8: Therefore, the total simple interest over 18 months is $7,125. Verification / Alternative check: You can think of it quarterly: 18 months is 6 quarters. Annual interest is (50,000 * 9.5) / 100 = $4,750. For 1.5 years, that is 4,750 * 1.5 = 7,125. This consistent approach confirms the previous result. Why Other Options Are Wrong: $8,125 and $9,125: Both are larger than the correct amount and would correspond to higher rates or compound interest, which are not given. $6,125: Too small and does not match 9.5% over 1.5 years. $7,500: Slightly larger than the correct interest and does not fit the exact calculation. Common Pitfalls: Some candidates mistakenly compound the interest quarterly or try to use a quarterly rate of 9.5 / 4% with compounding, which is not required here. Others forget to convert months to years before using the simple interest formula. Always read whether interest is simple or compound and handle time units carefully. Final Answer: The total simple interest earned over 18 months is $7,125.

Question 17

Hire-Purchase with Flat Simple Interest: A car is purchased on hire-purchase. The cash price is $21,000. The terms require a deposit of 10% of the cash price and the remaining balance to be paid over 60 equal monthly instalments. If interest is char…

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Introduction / Context: This question deals with a hire purchase agreement where the buyer pays a deposit and repays the balance with interest in equal monthly instalments. The interest is computed at a flat simple interest rate on the outstanding balance for the full term. You are asked to find the total cost of the car, including both the deposit and all interest charges. Given Data / Assumptions: Cash price of the car = $21,000. Deposit = 10% of cash price. Remaining balance is repaid over 60 months. Annual flat simple interest rate = 12% per annum on the outstanding balance. Term = 60 months = 5 years. Concept / Approach: First compute the deposit and outstanding balance. Then, because interest is flat and simple, it is calculated on the initial outstanding balance for the entire term, even though instalments gradually reduce the amount owed. The total cost of the car equals the deposit plus principal repaid plus total interest. We use I = (P * r * t) / 100 with P as the outstanding balance after the deposit and t = 5 years. Step-by-Step Solution: Step 1: Compute the deposit: 10% of 21,000 = 0.10 * 21,000 = $2,100. Step 2: Outstanding balance to be financed = 21,000 − 2,100 = $18,900. Step 3: Term of repayment = 60 months = 5 years. Step 4: Annual flat simple interest rate r = 12%. Step 5: Use the SI formula on the outstanding balance: I = (P * r * t) / 100. Step 6: I = (18,900 * 12 * 5) / 100. Step 7: First compute 12 * 5 = 60, so I = (18,900 * 60) / 100 = 18,900 * 0.6 = $11,340. Step 8: Total paid through instalments = principal financed + interest = 18,900 + 11,340 = $30,240. Step 9: Add the initial deposit to get the total cost: 30,240 + 2,100 = $32,340. Step 10: Therefore, the total cost of the car is $32,340. Verification / Alternative check: Check the logic: The buyer pays the full cash price (21,000) plus additional interest on the financed portion. Interest of $11,340 on an outstanding balance of $18,900 over 5 years at 12% flat is consistent with I = 18,900 * 0.12 * 5. Summing the deposit and all repayments gives a figure significantly above the cash price, which is typical of hire purchase deals. Why Other Options Are Wrong: $31,240 and $30,240: These omit part of the cost and are less than deposit + full flat interest. $33,600: Higher than the computed total and does not match the flat interest calculation. $29,240: Too low, not even equal to the sum of cash price and a modest interest. Common Pitfalls: Some learners only calculate interest on the cash price instead of the financed balance, while others wrongly apply reducing balance interest instead of flat simple interest. Another common error is forgetting to add back the initial deposit when computing the total cost. Always separate the steps: calculate deposit, financed balance, interest on that balance, then sum everything. Final Answer: The total cost of the car under this hire-purchase plan is $32,340.

Question 18

Flat-Rate Loan and Effective Interest: Jason takes a personal loan for 4 years with equal quarterly repayments. The lender quotes 12% per annum flat rate (simple interest) on the original principal. What is the approximate effective annual interest …

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Introduction / Context: This question explores the difference between a quoted flat rate of interest and the true effective annual interest rate on a loan repaid in equal instalments. Jason's loan carries a 12% per annum flat rate on the full principal, but payments are made quarterly over 4 years. You must compute the approximate effective annual rate implied by this structure using the concept of internal rate of return (IRR). Given Data / Assumptions: Flat simple interest rate = 12% per annum on the original principal. Loan term = 4 years. Repayments are equal and made quarterly (every 3 months). Total number of payments = 4 years × 4 quarters per year = 16 payments. We assume a principal of P = 1 (for rate calculation, any positive principal works proportionally). Concept / Approach: Under a flat rate, total interest over the entire term is computed on the original principal as I = (P * r_flat * t) / 100. This total interest is then spread evenly over all instalments. To find the effective rate, treat the loan as an investment by the lender: an initial outflow of P at time 0 and an inflow of equal instalments each quarter. Solve for the quarterly rate r_q that equates the present value of instalments to P, then convert r_q to an effective annual rate using (1 + r_q)^4 − 1. Step-by-Step Solution: Step 1: Assume principal P = 1 for convenience. Step 2: Flat rate r_flat = 12% per annum, term t = 4 years. Step 3: Total interest over the full term: I_total = (1 * 12 * 4) / 100 = 0.48. Step 4: Total amount repaid = principal + interest = 1 + 0.48 = 1.48. Step 5: Number of quarterly payments = 4 years × 4 = 16. Each instalment = 1.48 / 16 = 0.0925. Step 6: Let r_q be the effective quarterly rate. The present value of all instalments must equal the original principal: 0.0925 / (1 + r_q)^1 + 0.0925 / (1 + r_q)^2 + ... + 0.0925 / (1 + r_q)^16 = 1. Step 7: Solving this equation (using numerical methods) gives r_q ≈ 0.05035, i.e., about 5.04% per quarter. Step 8: Convert this to an effective annual rate: r_eff = (1 + r_q)^4 − 1 ≈ (1.05035)^4 − 1 ≈ 0.2171 or 21.71%. Verification / Alternative check: The flat rate of 12% per annum seems low, but because the borrower is repaying the principal gradually while paying interest as if the full principal were outstanding for the whole 4 years, the economic cost is much higher. An effective annual rate above 20% is typical for such flat rate loans, so 21.71% is a reasonable and consistent result. Why Other Options Are Wrong: 18.00% and 15.50%: These are below the computed effective rate and underestimate the true cost of the loan. 12.00%: This is just the flat rate and ignores the impact of declining principal due to instalments. 24.00%: Slightly higher than the computed IRR and not supported by the detailed present value calculation. Common Pitfalls: Many students mistakenly equate the flat rate with the effective rate or linearly scale the total interest over time without considering the timing of repayments. Others simply double the flat rate when payments are frequent, which is incorrect. The correct approach uses present value and internal rate of return concepts to reflect the actual cost of borrowing. Final Answer: The approximate effective annual interest rate implied by the flat-rate loan is 21.71% per annum.

Question 19

Exact-Time Simple Interest on a Short-Term Loan: A loan of $15,000 is taken at 7% per annum simple interest on April 7 and is due exactly 7 months later on November 7. Using exact time in days (April 7 to November 7 = 214 days) and a 365-day year, w…

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Introduction / Context: This problem involves simple interest calculated using exact time in days and a 365 day year. You must compute the interest for a specific number of days and then add it to the principal to obtain the maturity value. This type of calculation is common in financial mathematics for short term loans and notes. Given Data / Assumptions: Principal P = $15,000. Annual simple interest rate r = 7% per annum. Exact time from April 7 to November 7 = 214 days. A 365 day year is used for the time fraction. Concept / Approach: When using exact time and a 365 day year, the time in years is t = number of days / 365. Simple interest is then I = (P * r * t) / 100. After finding the interest, the total amount to be repaid (maturity value) is A = P + I. Careful handling of the day count and percentage conversions is essential to get the correct answer. Step-by-Step Solution: Step 1: Compute the time in years: t = 214 / 365. Step 2: Use the SI formula I = (P * r * t) / 100. Step 3: Substitute P = 15,000, r = 7, and t = 214 / 365. Step 4: I = (15,000 * 7 * 214) / (100 * 365). Step 5: Numerator = 15,000 * 7 * 214 = 22,470,000. Step 6: Denominator = 100 * 365 = 36,500. Step 7: I = 22,470,000 / 36,500 ≈ $615.52 (rounded to two decimal places). Step 8: Total amount A = P + I ≈ 15,000 + 615.52 = $15,615.52. Step 9: Therefore, the amount to be repaid is approximately $15,615.52. Verification / Alternative check: You can estimate to check reasonableness. Seven percent of $15,000 for a full year is 0.07 * 15,000 = $1,050. The fraction of the year is 214 / 365, which is a little more than half. Half of $1,050 is about $525, and taking the exact fraction gives around $615.52, which is consistent with the precise calculation. This confirms that the computed interest and repayment amount are sensible. Why Other Options Are Wrong: $13,615.52 and $14,615.52: These are less than the principal, which is impossible when positive interest is charged. $16,615.52: This would require about $1,615.52 in interest, far too high for 214 days at 7%. $15,500.00: This implies interest of only $500, lower than the accurate calculation. Common Pitfalls: Errors occur if you mistakenly treat 7 months as 7 / 12 of a year instead of using the given 214 days, or if you use a 360 day year instead of 365. Rounding too early or incorrectly handling the division can also cause small mismatches. Always follow the formula with the specified day count and year length. Final Answer: The total amount to be repaid on the due date is $15,615.52 (approximately).

Question 20

Time Required to Earn a Given Simple Interest: How long will it take $3,000 to earn $60 simple interest at 6% per annum, assuming simple interest and expressing the answer in months?

Accepted Answer

Introduction / Context: This problem asks you to determine the length of time required for a given principal to earn a specified amount of simple interest at a known annual rate. This is a basic time calculation using the simple interest formula, and the final answer must be expressed in months. Given Data / Assumptions: Principal P = $3,000. Desired interest I = $60. Annual simple interest rate r = 6% per annum. Interest is simple, not compound. Time t is unknown and must be expressed in months. Concept / Approach: The simple interest formula is I = (P * r * t) / 100, where t is in years. When you know I, P, and r, you can rearrange the formula to solve for t in years and then convert that value into months by multiplying by 12. This is one of the most straightforward applications of the SI formula. Step-by-Step Solution: Step 1: Write the SI formula: I = (P * r * t) / 100. Step 2: Substitute the known values: 60 = (3,000 * 6 * t) / 100. Step 3: Simplify the numerator: 3,000 * 6 = 18,000. Step 4: So 60 = (18,000 * t) / 100 = 180t. Step 5: Solve for t: t = 60 / 180 = 1 / 3 year. Step 6: Convert 1 / 3 year into months: (1 / 3) * 12 = 4 months. Step 7: Therefore, it will take 4 months to earn $60 in simple interest. Verification / Alternative check: At 6% per annum, yearly interest on $3,000 is (3,000 * 6) / 100 = $180. One third of this year is 4 months, and one third of the yearly interest is 180 / 3 = $60. This matches the required interest, confirming the result. Why Other Options Are Wrong: 2 months: This would correspond to t = 2 / 12 year, giving interest only $30. 3 months: This gives t = 1 / 4 year and interest $45, still less than $60. 5 months: Interest would be 5 / 12 of $180, about $75, which is too high. 6 months: This is half a year with interest $90, also too high. Common Pitfalls: Common mistakes include forgetting to divide by 100 in the SI formula or failing to convert the final time from years to months. Another error is simply guessing based on rough proportion instead of solving the equation exactly. Always follow the algebra and then convert units carefully. Final Answer: The required time is 4 months.

Simple Interest Questions