Question 1

What is the present value of ₹169 due in 2 years if money is compounded annually at 4% per annum? (That is, how much should be invested today to get ₹169 after 2 years at 4% compounded annually?)

Accepted Answer

Introduction: This question tests present value under compound interest. Present value is the amount that, when compounded at a given rate for a given time, becomes the future value. With annual compounding, we use PV = FV / (1 + r/100)^t. Here the future value is ₹169, rate is 4% per annum, and time is 2 years, so we compute the discount factor and divide. Given Data / Assumptions: Future value FV = ₹169 Rate r = 4% per annum compounded annually Time t = 2 years Present value formula: PV = FV / (1 + r/100)^t Concept / Approach: Compute compound growth factor for 2 years: (1.04)^2. Then divide the future value by this factor to get the present value. Since compounding is annual, no conversion of periods is needed. Step-by-Step Solution: PV = FV / (1 + r/100)^t PV = 169 / (1 + 4/100)^2 PV = 169 / (1.04)^2 (1.04)^2 = 1.0816 PV = 169 / 1.0816 = 156.25 Verification / Alternative check: Check by compounding: 156.25 * 1.04 = 162.50 (after 1 year). Then 162.50 * 1.04 = 169.00 (after 2 years). The result matches exactly, confirming the present value is correct. Why Other Options Are Wrong: ₹158.00 and ₹160.25 are too high and would compound to more than ₹169. ₹150.50 and ₹154.75 are too low and would compound to less than ₹169. Only ₹156.25 compounds to exactly ₹169 in 2 years at 4%. Common Pitfalls: Using simple interest discounting instead of compound discounting, forgetting to square the growth factor for 2 years, or using 0.04 incorrectly while also dividing by 100 again. Final Answer: The present value is ₹156.25.

Question 2

The simple interest on a sum of money is ₹50. What is the sum (principal)? I. The interest rate is 10% per annum. II. The sum earns this simple interest in 10 years. Which statement(s) are sufficient to determine the principal under simple interest?

Accepted Answer

Introduction: This is a data sufficiency question for simple interest where the interest amount is known but principal is not. Simple interest depends on principal P, rate r, and time t via SI = (P * r * t)/100. To determine P uniquely, we must know both r and t (or otherwise have enough information to infer them). The task is to check whether statement I or II alone is sufficient, or whether both are required. Given Data / Assumptions: Simple interest SI = ₹50 Statement I: r = 10% per annum Statement II: t = 10 years Formula: SI = (P * r * t) / 100 Concept / Approach: Evaluate sufficiency of each statement. If only r is known, then SI = (P * r * t)/100 still has two unknowns (P and t). If only t is known, it has two unknowns (P and r). Only when both r and t are known can we solve uniquely for P using P = (SI * 100) / (r * t). Step-by-Step Solution: Using SI = (P * r * t)/100 Check Statement I alone: r = 10%, but t is unknown, so P cannot be uniquely found. Check Statement II alone: t = 10 years, but r is unknown, so P cannot be uniquely found. Using I and II together: r = 10 and t = 10 P = (SI * 100) / (r * t) = (50 * 100) / (10 * 10) = 5000 / 100 = 50 Verification / Alternative check: If P = ₹50 at 10% for 10 years, SI = (50 * 10 * 10)/100 = 50, matching the given interest. This confirms that with both statements, the principal is uniquely determined. Why Other Options Are Wrong: Options claiming I alone or II alone is sufficient are incorrect because each leaves two unknowns. “Either I or II alone” is also incorrect for the same reason. “Even together not sufficient” is false because together they give an exact P. Common Pitfalls: Assuming a default time or rate, confusing simple interest with compound interest, or thinking that knowing SI and one of r or t automatically fixes P (it does not). Final Answer: Both I and II are necessary to determine the principal.

Question 3

Find the simple interest charged on borrowing $325 for 5 years at a simple interest rate of 3% per annum.

Accepted Answer

Introduction: This question tests direct calculation of simple interest when principal, rate, and time are provided. Simple interest is computed as SI = (P * r * t)/100. Since all quantities are already in compatible units (rate per annum and time in years), it is a straightforward one-step substitution and is therefore easy difficulty. Given Data / Assumptions: Principal P = $325 Rate r = 3% per annum Time t = 5 years Formula: SI = (P * r * t) / 100 Concept / Approach: Substitute P, r, and t into the simple interest formula. Multiply principal by rate and time, then divide by 100 to convert percentage into a fraction of 1. Step-by-Step Solution: SI = (P * r * t) / 100 SI = (325 * 3 * 5) / 100 SI = (325 * 15) / 100 SI = 4875 / 100 SI = 48.75 Verification / Alternative check: Yearly interest at 3% on $325 is 0.03 * 325 = $9.75. Over 5 years, interest = 9.75 * 5 = $48.75, matching the formula result. Why Other Options Are Wrong: $46.00 and $34.75 are too low, usually coming from wrong multiplication or wrong percentage handling. $59.00 is too high. $52.00 is a plausible distractor but does not match the exact computation. Common Pitfalls: Forgetting to divide by 100, using 3 as 0.3, or mistakenly compounding interest. Another mistake is multiplying by 5 twice or not at all. Final Answer: The simple interest charged is $48.75.

Question 4

You invest $750 into a certificate of deposit at a simple annual interest rate of 4%, and you receive the interest at the end of each year (simple interest). How many years will it take to earn a total of $150 in simple interest?

Accepted Answer

Introduction: This question tests finding time in a simple interest situation. Under simple interest, interest accumulates at a constant amount each year: yearly interest = (P * r)/100. Since the interest is paid out annually and does not compound, we can either use the standard formula SI = (P * r * t)/100 or compute yearly interest and divide the required total interest by that yearly amount. Given Data / Assumptions: Principal P = $750 Annual simple interest rate r = 4% per annum Total simple interest needed SI = $150 Time = t years (unknown) Formula: SI = (P * r * t) / 100 Concept / Approach: Rearrange the simple interest formula to solve for time: t = (SI * 100) / (P * r). Alternatively, compute interest per year and then compute how many years are needed to reach $150. Both methods should agree because simple interest is linear in time. Step-by-Step Solution: SI = (P * r * t) / 100 t = (SI * 100) / (P * r) t = (150 * 100) / (750 * 4) t = 15000 / 3000 t = 5 Verification / Alternative check: Yearly interest = 4% of 750 = 0.04 * 750 = $30 per year. To earn $150, years = 150 / 30 = 5 years. This matches the formula result. Why Other Options Are Wrong: 4 years gives only $120 (4 * 30). 6, 7, and 8 years give $180, $210, and $240 respectively, which exceed $150. Only 5 years produces exactly $150 in simple interest. Common Pitfalls: Accidentally compounding interest, using 4 as 0.4, forgetting to divide by 100, or thinking the principal changes because interest is paid out (principal remains $750 in a simple interest setup). Final Answer: It will take 5 years to earn $150 in simple interest.

Question 5

On retirement, a woman receives Rs 1,45,440 from her provident fund and invests the entire amount in a scheme that pays 20% simple interest per annum; based on this simple interest income, what fixed monthly amount will she receive as regular income…

Accepted Answer

Introduction / Context: This aptitude question on simple interest connects retirement planning with regular income from a lump sum provident fund. The woman invests her entire retirement amount in a scheme that pays a fixed rate of simple interest per year. The key idea is that the interest earned in one year can be converted into a constant monthly income by dividing the annual interest by twelve months. Given Data / Assumptions: - Principal invested in the simple interest scheme = Rs 1,45,440. - Annual simple interest rate = 20 percent per annum. - Interest is calculated using simple interest, not compound interest. - Required quantity is the fixed monthly income generated only from interest, with the principal assumed to remain invested. Concept / Approach: The basic simple interest formula is SI = (P * R * T) / 100, where P is principal, R is annual rate of interest in percent, and T is time in years. Here we first compute the simple interest for one year, because the rate is given per annum. Once we know the yearly interest, we divide it by 12 to find the monthly interest income, which equals the fixed monthly income from the scheme. Step-by-Step Solution: Step 1: Identify principal P = Rs 1,45,440. Step 2: Identify annual rate R = 20 percent per annum. Step 3: For one year, T = 1 year. Step 4: Compute annual simple interest: SI = (P * R * T) / 100 = (1,45,440 * 20 * 1) / 100. Step 5: Calculate the value: 1,45,440 * 20 = 2,90,880, then divide by 100 to get SI = Rs 29,088 per year. Step 6: Convert this annual interest to monthly income by dividing by 12: monthly income = 29,088 / 12. Step 7: Perform the division: 29,088 / 12 = Rs 2,424 per month. Verification / Alternative check: We can verify by reversing the calculation. If she receives Rs 2,424 per month, then in one full year she receives 2,424 * 12 = 29,088 as interest. Dividing this annual interest by the principal 1,45,440 and multiplying by 100 gives the annual rate: (29,088 * 100) / 1,45,440 = 20 percent. This matches the given rate, so our monthly income value is consistent and correct. Why Other Options Are Wrong: Rs 2,380 is lower than the correct income and could arise from rounding or using an incorrect principal or rate. Rs 2,550 is higher than the correct amount and does not match the exact simple interest calculation at 20 percent. Rs 2,224 would correspond to a lower annual interest rate than 20 percent and therefore does not satisfy the given conditions. Only Rs 2,424 correctly corresponds to 20 percent simple interest on Rs 1,45,440. Common Pitfalls: A common mistake is to divide the principal directly by 12 instead of dividing the annual interest by 12. Some learners also forget that the rate is per year and may try to apply 20 percent directly on a monthly basis, which is incorrect in simple interest problems. Another error is rounding intermediate values instead of using exact arithmetic, which can lead to a different monthly figure. Careful use of the formula and proper conversion from yearly to monthly income avoids these issues. Final Answer: The fixed monthly income she receives from the simple interest investment is Rs 2,424.

Question 6

Praveena takes a loan of Rs 1,200 at simple interest for as many years as the numerical value of the rate of interest; if she pays a total of Rs 432 as interest at the end of the loan period, what is the annual simple interest rate in percent per an…

Accepted Answer

Introduction / Context: This simple interest question links the time of a loan and the rate of interest by saying that the number of years is equal to the numerical value of the rate. Such questions test a candidate's ability to form an equation from the symbolic statement and then solve for the rate using the simple interest formula. The situation is realistic for bank loans and small personal borrowings in aptitude exams. Given Data / Assumptions: - Principal borrowed P = Rs 1,200. - Total simple interest paid SI = Rs 432. - Let the annual simple interest rate be R percent. - Time period T in years is equal to the numerical value of R, so T = R years. - Interest is calculated using the simple interest formula only. Concept / Approach: The standard simple interest formula is SI = (P * R * T) / 100. Here, the key relationship is T = R. Substituting T with R in the formula gives SI = (P * R * R) / 100, which is SI = (P * R^2) / 100. Using the known values of SI and P, we can solve for R^2 and then take the positive square root to get the annual simple interest rate in percent. Step-by-Step Solution: Step 1: Write the simple interest formula: SI = (P * R * T) / 100. Step 2: Use the condition T = R, so SI = (P * R^2) / 100. Step 3: Substitute known values: 432 = (1,200 * R^2) / 100. Step 4: Multiply both sides by 100 to clear the denominator: 432 * 100 = 1,200 * R^2. Step 5: Compute the left side: 432 * 100 = 43,200. Step 6: Divide both sides by 1,200: R^2 = 43,200 / 1,200 = 36. Step 7: Take the positive square root (rate cannot be negative): R = square root of 36 = 6. Step 8: Therefore, the annual simple interest rate is 6 percent per annum. Verification / Alternative check: To verify, use R = 6 percent and T = 6 years in the simple interest formula. Compute SI = (1,200 * 6 * 6) / 100. First 1,200 * 6 = 7,200, then 7,200 * 6 = 43,200. Dividing by 100 gives SI = Rs 432. This matches the given interest, so the calculated rate of 6 percent per annum is correct. Why Other Options Are Wrong: A rate of 7 percent would give SI = (1,200 * 7 * 7) / 100 = 588, which is larger than Rs 432. A rate of 9 percent gives SI = (1,200 * 9 * 9) / 100 = 972, which is also incorrect. A rate of 11 percent produces even higher interest, far from the given Rs 432. Only 6 percent leads to exactly the required interest amount. Common Pitfalls: Learners sometimes treat T as 1 year or misread the statement and take T equal to interest instead of the numerical value of the rate. Another frequent error is to forget that R is in percent, which leads to missing the division by 100 in the formula. Ensuring that the relationship T = R is used correctly and carefully handling the equation avoids these mistakes. Final Answer: The annual simple interest rate on Praveena's loan is 6% per annum.

Question 7

Lasya invests two different sums of money at simple interest, one at 5% per annum and the other at 4% per annum; if the simple interest earned from both investments is equal, what is the ratio of Lasya's investments at 5% and at 4%?

Accepted Answer

Introduction / Context: This question checks understanding of how simple interest depends on principal, rate, and time. Lasya invests two different amounts at two different annual simple interest rates, yet the interest earned from each investment is the same. The problem asks for the ratio of the two principal amounts, which is a standard concept used in aptitude exams on simple interest and proportional reasoning. Given Data / Assumptions: - Investment 1 earns simple interest at 5 percent per annum. - Investment 2 earns simple interest at 4 percent per annum. - The simple interest earned from both investments is equal. - The time period for both investments is assumed to be the same. - Required ratio = amount invested at 5 percent : amount invested at 4 percent. Concept / Approach: For simple interest, SI = (P * R * T) / 100. When the time T is the same for both investments and the interests are equal, the products P1 * R1 and P2 * R2 must be equal. Therefore P1 * R1 = P2 * R2. From this, the ratio of the principals is P1 / P2 = R2 / R1. This means the principal is inversely proportional to the rate when interest and time are the same. Step-by-Step Solution: Step 1: Let the amount invested at 5 percent be P1. Step 2: Let the amount invested at 4 percent be P2. Step 3: Simple interest for P1 is SI1 = (P1 * 5 * T) / 100. Step 4: Simple interest for P2 is SI2 = (P2 * 4 * T) / 100. Step 5: Given that SI1 = SI2, so (P1 * 5 * T) / 100 = (P2 * 4 * T) / 100. Step 6: Cancel common factors 100 and T (T is nonzero), giving 5 * P1 = 4 * P2. Step 7: Rearranging, P1 / P2 = 4 / 5. Step 8: Hence, the ratio of investments at 5 percent and 4 percent is 4 : 5. Verification / Alternative check: Choose simple values that satisfy the ratio 4 : 5. For example, let P1 = Rs 4,000 and P2 = Rs 5,000 and take a common time of 1 year. Then SI1 = (4,000 * 5 * 1) / 100 = Rs 200 and SI2 = (5,000 * 4 * 1) / 100 = Rs 200. The interests are equal, confirming that the ratio 4 : 5 is correct. Why Other Options Are Wrong: A ratio of 5 : 4 would imply P1 / P2 = 5 / 4, which would make the interest at 5 percent larger than at 4 percent, contradicting the condition of equal interest. Ratios 7 : 6 and 6 : 7 are arbitrary and do not satisfy the necessary inverse proportionality between principal and rate. Only the ratio 4 : 5 correctly balances the higher rate with a smaller principal. Common Pitfalls: A typical mistake is to assume that the ratio of principals is the same as the ratio of rates, rather than the inverse. Another error is forgetting that the time is the same for both investments and therefore not cancelling it properly. Remember that for equal simple interest over equal time, principal is inversely proportional to the rate of interest. Final Answer: The ratio of Lasya's investments at 5 percent and 4 percent is 4 : 5.

Question 8

A person invests a certain sum of money for two years at an annual rate of 8% and finds that the amount received under compound interest is Rs 48 more than the amount that would have been received under simple interest; what is the original principa…

Accepted Answer

Introduction / Context: This question compares compound interest and simple interest on the same principal, rate, and time. Over two years, compound interest yields a slightly higher amount than simple interest, and the difference in the amounts is given as Rs 48. The task is to work backwards from this difference to find the original principal invested. Such problems test understanding of both interest types and the special relation between them for a two year period. Given Data / Assumptions: - Principal invested = P (unknown). - Annual rate of interest R = 8 percent per annum. - Time period T = 2 years. - Amount with compound interest exceeds the amount with simple interest by Rs 48. - Interest is calculated annually, with compounding once per year. Concept / Approach: For simple interest over two years, total interest is SI = (P * R * T) / 100. For compound interest compounded annually, amount after two years is A = P * (1 + R / 100)^2. The difference between compound interest and simple interest for two years at the same rate is a known relation: CI − SI = P * (R^2) / 100^2. Using this relation, we can directly equate P * (R^2) / 100^2 to the given difference and solve for P. Step-by-Step Solution: Step 1: Note the relation for two years: CI − SI = P * (R^2) / 100^2. Step 2: Here, CI − SI = Rs 48 and R = 8 percent. Step 3: Substitute values: 48 = P * (8^2) / 100^2. Step 4: Compute 8^2 = 64, so 48 = P * 64 / 10,000. Step 5: Rearrange to solve for P: P = 48 * 10,000 / 64. Step 6: Compute 48 * 10,000 = 4,80,000. Step 7: Divide: 4,80,000 / 64 = 7,500. Step 8: Therefore, the original principal is P = Rs 7,500. Verification / Alternative check: Using P = Rs 7,500, compute simple and compound interest. Simple interest for two years: SI = (7,500 * 8 * 2) / 100 = (7,500 * 16) / 100 = 1,20,000 / 100 = Rs 1,200. Amount with simple interest = 7,500 + 1,200 = 8,700. For compound interest, amount A = 7,500 * (1 + 8 / 100)^2 = 7,500 * (1.08)^2. Now (1.08)^2 = 1.1664, so A = 7,500 * 1.1664 = Rs 8,748. The difference A − 8,700 = 8,748 − 8,700 = Rs 48, which matches the given data. Why Other Options Are Wrong: If P were Rs 8,000, the difference between compound and simple interest at 8 percent for two years would be 8,000 * 64 / 10,000 = Rs 51.20, not Rs 48. For P = 6,500, the difference becomes 6,500 * 64 / 10,000 = Rs 41.60. For P = 5,000, the difference is 5,000 * 64 / 10,000 = Rs 32. None of these equal the required Rs 48. Only P = Rs 7,500 satisfies the condition exactly. Common Pitfalls: Learners often compute full compound and simple interest amounts separately and may make arithmetic errors, instead of using the compact relation for two years. Another error is to apply the relation for a wrong time period or wrong rate. Forgetting to square the rate in the special formula CI − SI = P * R^2 / 100^2 also leads to incorrect results. Using the standard relation carefully avoids unnecessary complications. Final Answer: The original principal sum invested is Rs 7,500.

Question 9

A lady borrows a certain principal amount from a bank at 12% simple interest per annum and after 3 years finds that she has paid Rs 5,400 as interest only; what was the original principal amount borrowed from the bank under this simple interest agre…

Accepted Answer

Introduction / Context: This is a straightforward simple interest problem where the total interest paid over a fixed time and rate is known and the task is to find the original principal borrowed. Such questions are common in aptitude tests to check whether candidates can rearrange the simple interest formula to solve for the principal. The context of a bank loan makes the scenario realistic and relatable. Given Data / Assumptions: - Total simple interest paid SI = Rs 5,400. - Annual simple interest rate R = 12 percent per annum. - Time period T = 3 years. - Principal P (the amount borrowed) is unknown. - Interest is calculated strictly using the simple interest formula. Concept / Approach: The basic formula for simple interest is SI = (P * R * T) / 100. Here we need to find P, so we rearrange the formula to P = (SI * 100) / (R * T). By substituting the given values of SI, R, and T into this rearranged formula, we can compute the original loan amount. No compounding or additional charges are involved in this idealised calculation. Step-by-Step Solution: Step 1: Start from SI = (P * R * T) / 100. Step 2: Rearrange to find principal: P = (SI * 100) / (R * T). Step 3: Substitute SI = 5,400, R = 12, and T = 3. Step 4: Compute denominator R * T = 12 * 3 = 36. Step 5: Compute numerator SI * 100 = 5,400 * 100 = 5,40,000. Step 6: Divide: P = 5,40,000 / 36. Step 7: Perform the division: 5,40,000 / 36 = 15,000. Step 8: Therefore, the principal amount borrowed from the bank is Rs 15,000. Verification / Alternative check: Verify by computing the simple interest on P = Rs 15,000 for 3 years at 12 percent per annum. SI = (15,000 * 12 * 3) / 100. First 15,000 * 12 = 1,80,000. Then 1,80,000 * 3 = 5,40,000. Dividing by 100 gives SI = Rs 5,400, which matches the interest given in the question. This confirms that the calculated principal is correct. Why Other Options Are Wrong: If P were Rs 1,50,000, the interest would be ten times larger, that is Rs 54,000, not Rs 5,400. A principal of Rs 1,500 would give SI = (1,500 * 12 * 3) / 100 = Rs 540, which is too small. A principal of Rs 1,62,000 would produce an interest far greater than Rs 5,400. Only Rs 15,000 leads to the correct interest amount. Common Pitfalls: Some learners mistakenly divide by 100 twice or forget to multiply the interest by 100 while isolating the principal. Others may mix up the roles of SI and P in the formula. Writing the rearranged expression P = SI * 100 / (R * T) clearly before substituting values helps avoid such algebraic errors. Final Answer: The original principal amount borrowed from the bank is Rs 15,000.

Question 10

At what annual rate of simple interest will a principal of Rs 415 grow to an amount of Rs 514 in 4 years, assuming interest is calculated using the simple interest formula only?

Accepted Answer

Introduction / Context: This question asks for the annual simple interest rate that causes a principal to grow to a given amount over a fixed time. It tests the ability to extract the interest earned from the final amount and then use the simple interest formula to find the rate of interest. Problems of this type are very common in aptitude tests and financial arithmetic. Given Data / Assumptions: - Principal P = Rs 415. - Final amount A after 4 years = Rs 514. - Time period T = 4 years. - Interest is paid using simple interest, not compound interest. - Annual rate of simple interest R percent per annum is to be found. Concept / Approach: In simple interest, the amount A after T years is given by A = P + SI, where SI is simple interest. First we compute SI as A minus P. Then we use the formula SI = (P * R * T) / 100 and rearrange to get R = (SI * 100) / (P * T). Substituting the known values for SI, P, and T yields the required rate in percent per annum. Step-by-Step Solution: Step 1: Compute the interest earned: SI = A − P = 514 − 415. Step 2: Calculate 514 − 415 = 99, so SI = Rs 99. Step 3: Use the simple interest formula SI = (P * R * T) / 100. Step 4: Rearrange for R: R = (SI * 100) / (P * T). Step 5: Substitute SI = 99, P = 415, T = 4. Step 6: Compute numerator: 99 * 100 = 9,900. Step 7: Compute denominator: 415 * 4 = 1,660. Step 8: Divide to get R: R = 9,900 / 1,660 which is approximately 5.963855 percent. Step 9: Rounding to two decimal places, R is approximately 5.96 percent per annum. Verification / Alternative check: To verify, assume R = 5.96 percent and recompute the simple interest. SI = (415 * 5.96 * 4) / 100. First, 415 * 5.96 ≈ 2,474. Then 2,474 * 4 ≈ 9,896 and dividing by 100 gives about Rs 98.96, which is extremely close to Rs 99, the required interest. The small difference is due to rounding; hence 5.96 percent is the best match among the given options. Why Other Options Are Wrong: A rate of 4.58 percent gives SI = (415 * 4.58 * 4) / 100, which is much less than Rs 99. A rate of 6.52 percent gives SI higher than Rs 99. Similarly, 4.98 percent also produces interest significantly different from 99 when substituted into the formula. Only 5.96 percent generates an interest amount that matches the difference between 514 and 415. Common Pitfalls: Candidates sometimes forget to subtract the principal from the final amount and mistakenly treat A as SI. Another error is to use time in months rather than years or to round too early in the calculation, leading to inaccurate results. Keeping all intermediate values in exact fractional or decimal form until the final step yields a more accurate rate. Final Answer: The required annual rate of simple interest is approximately 5.96% per annum.

Question 11

A sum of money is invested at a simple interest rate of 7.5% per annum for 4 years, and if the same sum were invested for 5 years the interest would increase by Rs 375; what was the initial principal amount invested in this simple interest situation?

Accepted Answer

Introduction / Context: This question uses the idea that in simple interest, the interest amount is directly proportional to time. The same principal and rate are applied, but the time is increased from 4 years to 5 years. The extra year of investment adds a known additional interest of Rs 375. By using this extra year of interest, we can determine the principal. This is a common style of shortcut problem in simple interest chapters. Given Data / Assumptions: - Simple interest rate R = 7.5 percent per annum. - Original time T1 = 4 years. - New time T2 = 5 years. - Increase in interest when time increases by one year = Rs 375. - Principal P is unknown and constant across both cases. Concept / Approach: For simple interest, SI = (P * R * T) / 100. Since principal and rate are unchanged, the interest is directly proportional to time. The difference in interest between 5 years and 4 years is simply the interest for 1 extra year. Therefore extra interest = (P * R * 1) / 100. Setting this equal to Rs 375 allows us to solve for P directly without computing full interest for multiple years. Step-by-Step Solution: Step 1: Extra time between the two cases is 1 year (5 − 4). Step 2: Extra interest for that 1 year is given as Rs 375. Step 3: For 1 year, simple interest SI1 = (P * R * 1) / 100. Step 4: Substitute R = 7.5 percent and SI1 = 375. Step 5: Write the equation: 375 = (P * 7.5 * 1) / 100. Step 6: Rearrange for P: P = (375 * 100) / 7.5. Step 7: Compute numerator: 375 * 100 = 37,500. Step 8: Divide: 37,500 / 7.5 = 5,000. Step 9: Therefore, the principal invested is Rs 5,000. Verification / Alternative check: Using P = Rs 5,000, compute interest for 4 and 5 years. For 4 years, SI4 = (5,000 * 7.5 * 4) / 100. First 5,000 * 7.5 = 37,500, then multiply by 4 to get 1,50,000, and divide by 100 to get Rs 1,500. For 5 years, SI5 = (5,000 * 7.5 * 5) / 100 = (37,500 * 5) / 100 = 1,87,500 / 100 = Rs 1,875. The difference SI5 − SI4 = 1,875 − 1,500 = Rs 375, which matches the given increase in interest. Why Other Options Are Wrong: If P were Rs 4,750, interest for one extra year would be (4,750 * 7.5 * 1) / 100 = Rs 356.25, not Rs 375. For P = Rs 4,500, extra interest would be Rs 337.50. For P = Rs 3,750, extra interest would be Rs 281.25. None of these equal the stated increase of Rs 375. Only Rs 5,000 yields the correct additional interest for the extra year. Common Pitfalls: A common mistake is to compute full interest for both 4 and 5 years separately without noticing that a one year shortcut exists. Another error is to treat 7.5 percent as 0.75 instead of 7.5 divided by 100. Remember that for simple interest, the extra interest due to an extra year is directly proportional to the principal and rate only. Final Answer: The initial principal amount invested was Rs 5,000.

Question 12

Deksha borrows Rs 500 at 5% simple interest per annum; what total amount in rupees will she have to pay back in order to clear her debt after 4 years, assuming standard simple interest calculations?

Accepted Answer

Introduction / Context: This question is an elementary example of simple interest where the principal, rate, and time are given and we must find the total amount to be repaid. It checks whether the learner can correctly compute the interest and then add it to the original principal to find the sum owed after a fixed period. Such problems mimic small personal loans and short term borrowings. Given Data / Assumptions: - Principal borrowed P = Rs 500. - Annual simple interest rate R = 5 percent per annum. - Time period T = 4 years. - Interest is computed using the simple interest formula. - Required quantity is the total amount A = principal + interest. Concept / Approach: Simple interest is calculated using SI = (P * R * T) / 100. Once SI is known, the total amount to be repaid is A = P + SI. There is no compounding in simple interest, so the interest each year is constant and directly proportional to time. The key steps are to compute SI correctly and not to confuse interest alone with the total amount. Step-by-Step Solution: Step 1: Identify P = Rs 500, R = 5 percent, T = 4 years. Step 2: Use SI = (P * R * T) / 100. Step 3: Substitute the values: SI = (500 * 5 * 4) / 100. Step 4: Compute 500 * 5 = 2,500. Step 5: Multiply 2,500 * 4 = 10,000. Step 6: Divide by 100: SI = 10,000 / 100 = Rs 100. Step 7: Compute total amount A = P + SI = 500 + 100. Step 8: A = Rs 600. Step 9: So Deksha must repay Rs 600 to clear the debt after 4 years. Verification / Alternative check: As a quick check, we can calculate the interest per year. For one year, interest is (500 * 5 * 1) / 100 = Rs 25. Over 4 years, total interest is 25 * 4 = Rs 100, which agrees with the detailed calculation. Adding back the principal of Rs 500 gives a total of Rs 600, confirming the answer. Why Other Options Are Wrong: Rs 150 represents only part of the interest or a miscalculated interest amount and does not include the principal. Rs 650 would require interest of Rs 150, which does not match 5 percent of 500 over 4 years. Rs 100 is only the interest, not the total repayment amount. Only Rs 600 equals principal plus correctly calculated interest. Common Pitfalls: A frequent mistake is to choose the interest amount instead of the total repayment. Another error is to forget to divide by 100 in the simple interest formula when applying the percentage rate. Keeping the two steps separate, first finding SI and then adding it to the principal, helps avoid confusion. Final Answer: The total amount Deksha must pay back after 4 years is Rs 600.

Question 13

The simple interest accrued on an amount of Rs 28,500 over a period of 7 years is Rs 23,940; what is the annual rate of simple interest in percent per annum for this investment?

Accepted Answer

Introduction / Context: This problem provides the principal, the time period, and the total simple interest earned, and asks for the annual simple interest rate. It tests direct use of the simple interest formula rearranged to solve for the rate. Such questions are typical when analysing bank deposits, loans, or fixed deposits in aptitude and competitive exams. Given Data / Assumptions: - Principal P = Rs 28,500. - Simple interest earned SI = Rs 23,940. - Time period T = 7 years. - Annual rate of simple interest R in percent per annum is unknown. - Interest is calculated using simple interest, no compounding is involved. Concept / Approach: The simple interest formula SI = (P * R * T) / 100 can be rearranged to find the rate as R = (SI * 100) / (P * T). By plugging in the known values for SI, P, and T, we directly compute the percentage rate. Because all values are whole numbers, the calculation is straightforward and the result is a clean percentage. Step-by-Step Solution: Step 1: Start with SI = (P * R * T) / 100. Step 2: Rearrange for R: R = (SI * 100) / (P * T). Step 3: Substitute SI = 23,940, P = 28,500, T = 7. Step 4: Compute denominator P * T = 28,500 * 7 = 1,99,500. Step 5: Compute numerator SI * 100 = 23,940 * 100 = 23,94,000. Step 6: Divide numerator by denominator: R = 23,94,000 / 1,99,500. Step 7: Perform the division: 23,94,000 / 1,99,500 = 12. Step 8: Therefore, R = 12 percent per annum. Verification / Alternative check: Verify by recomputing the simple interest using R = 12 percent. SI = (28,500 * 12 * 7) / 100. First 28,500 * 12 = 3,42,000. Then 3,42,000 * 7 = 23,94,000. Dividing by 100 gives SI = Rs 23,940, which exactly matches the given interest. Hence, the rate of 12 percent per annum is confirmed as correct. Why Other Options Are Wrong: At 10.5 percent, SI would be (28,500 * 10.5 * 7) / 100, which is significantly less than Rs 23,940. At 12.5 percent, the interest would be slightly larger than 23,940. At 11 percent, interest is again lower than needed. Only 12 percent produces exactly Rs 23,940 over 7 years on Rs 28,500. Common Pitfalls: Candidates sometimes forget to multiply by 100 in the numerator when solving for R, which gives a rate that is too small. Another mistake is to divide the simple interest by time alone instead of by principal times time. Writing the formula explicitly and substituting step by step helps prevent these errors. Final Answer: The annual rate of simple interest is 12% per annum.

Question 14

A certain sum of money amounts to Rs 918 in 2 years and Rs 969 in 3.5 years at simple interest; what is the annual rate of simple interest in percent per annum for this sum?

Accepted Answer

Introduction / Context: This question provides the total amounts at two different times for the same principal under simple interest. The aim is to use the difference between the amounts to work out the yearly interest and then derive the annual rate. It tests understanding that under simple interest, the interest grows linearly with time and that amount is principal plus interest. Given Data / Assumptions: - Amount after 2 years, A2 = Rs 918. - Amount after 3.5 years, A3.5 = Rs 969. - The principal P is the same in both cases. - Interest is calculated using simple interest. - Required quantity is the annual simple interest rate R in percent per annum. Concept / Approach: Under simple interest, amount A = P + SI, where SI = (P * R * T) / 100. The difference between amounts at two times represents the interest earned during the additional time interval. Here, the difference between 3.5 years and 2 years is 1.5 years. By subtracting the two amounts, we directly compute the interest for 1.5 years. Dividing this interest by 1.5 gives the interest per year. Then we use the yearly interest and principal to find the annual rate. Step-by-Step Solution: Step 1: Compute the difference between the two amounts: A3.5 − A2 = 969 − 918. Step 2: 969 − 918 = 51, so interest for the extra 1.5 years is Rs 51. Step 3: Interest per year = 51 / 1.5. Step 4: Compute 51 / 1.5 = 34, so yearly simple interest is Rs 34. Step 5: Use A2 to find principal: A2 = P + SI for 2 years. Step 6: SI for 2 years = 2 * yearly interest = 2 * 34 = Rs 68. Step 7: Therefore P = A2 − SI2 = 918 − 68 = Rs 850. Step 8: Now yearly interest is Rs 34 on principal Rs 850, so use R = (SI per year * 100) / P. Step 9: R = (34 * 100) / 850 = 3,400 / 850 = 4. Step 10: Thus R = 4 percent per annum. Verification / Alternative check: Check with P = 850 and R = 4 percent. For 2 years, SI2 = (850 * 4 * 2) / 100 = (850 * 8) / 100 = 6,800 / 100 = Rs 68, so A2 = 850 + 68 = 918, which matches the first amount. For 3.5 years, SI3.5 = (850 * 4 * 3.5) / 100 = (850 * 14) / 100 = 11,900 / 100 = Rs 119, giving A3.5 = 850 + 119 = 969, matching the second amount. This confirms that 4 percent is correct. Why Other Options Are Wrong: If R were 5 percent, the yearly interest would be (850 * 5) / 100 = 42.50, which does not fit the observed increase of Rs 51 over 1.5 years. At 6 percent or 8 percent, the interest per year is even larger and would produce amounts that do not match Rs 918 and Rs 969. Only 4 percent leads to both amounts being consistent with simple interest growth. Common Pitfalls: Some learners incorrectly treat the difference between amounts as the yearly interest instead of interest over the extra time. Others forget that 3.5 years is 1.5 years more than 2 years and miscalculate the interval. Carefully computing interest over the additional time and then converting it to an annual figure avoids these mistakes. Final Answer: The annual rate of simple interest is 4% per annum.

Question 15

Deepinder lends Rs 8,200 to Jairaj for 16 years and Rs 4,900 to Karna for 15 years, both at the same annual rate of simple interest; if he receives Rs 19,446.50 in total as interest, what is the simple interest rate per annum?

Accepted Answer

Introduction / Context: This question combines two different simple interest loans made at the same rate but for different principals and time periods. The total interest from both loans over their entire durations is given, and the task is to find the common annual rate of interest. This type of problem checks whether learners can sum the interests and treat the common rate as a single unknown for the entire situation. Given Data / Assumptions: - Loan to Jairaj: principal P1 = Rs 8,200, time T1 = 16 years. - Loan to Karna: principal P2 = Rs 4,900, time T2 = 15 years. - Annual simple interest rate R percent is the same for both loans. - Total interest from both loans SI total = Rs 19,446.50. - Interest is calculated using simple interest, without compounding. Concept / Approach: Simple interest on each loan is SI1 = (P1 * R * T1) / 100 and SI2 = (P2 * R * T2) / 100. The total interest is SI total = SI1 + SI2. Since the rate R is common, factor R out and express SI total as R * (P1 * T1 + P2 * T2) / 100. Then solve for R using the known total interest and the sum P1 * T1 + P2 * T2. This gives the annual rate in percent per annum. Step-by-Step Solution: Step 1: Write total interest as SI total = (P1 * R * T1) / 100 + (P2 * R * T2) / 100. Step 2: Factor R / 100: SI total = (R / 100) * (P1 * T1 + P2 * T2). Step 3: Compute P1 * T1 = 8,200 * 16. Step 4: 8,200 * 16 = 1,31,200. Step 5: Compute P2 * T2 = 4,900 * 15 = 73,500. Step 6: Sum them: P1 * T1 + P2 * T2 = 1,31,200 + 73,500 = 2,04,700. Step 7: Use SI total = 19,446.50, so 19,446.50 = (R / 100) * 2,04,700. Step 8: Rearrange for R: R = (19,446.50 * 100) / 2,04,700. Step 9: Compute numerator: 19,446.50 * 100 = 19,44,650. Step 10: Divide: 19,44,650 / 2,04,700 = 9.5. Step 11: Thus R = 9.5 percent per annum. Verification / Alternative check: Check the interest on each loan with R = 9.5 percent. SI1 = (8,200 * 9.5 * 16) / 100. First 8,200 * 9.5 = 77,900, then multiply by 16 to get 12,46,400, divide by 100 to get Rs 12,464. SI2 = (4,900 * 9.5 * 15) / 100. Here 4,900 * 9.5 = 46,550, multiply by 15 to get 6,98,250 and divide by 100 to get Rs 6,982.50. Total interest = 12,464 + 6,982.50 = Rs 19,446.50, which matches the given total. Why Other Options Are Wrong: At 10 percent, the total interest would be higher than 19,446.50. At 10.5 percent or 11 percent, the total interest becomes even larger. Only the rate of 9.5 percent yields a combined interest equal to Rs 19,446.50, so the other options do not fit the total interest condition. Common Pitfalls: Some learners incorrectly average the rates or times instead of using the weighted sum P1 * T1 + P2 * T2. Others may forget to include one of the loans in the total interest calculation. Treating the total interest expression systematically and solving for R ensures an accurate answer. Final Answer: The simple interest rate per annum is 9.5% per year.

Question 16

A moneylender lends Rs 400 to one person for 3 years and Rs 500 to another person for 4 years at the same annual rate of simple interest; if the total interest received from both loans together is Rs 160, what is the rate of simple interest per annu…

Accepted Answer

Introduction / Context: This problem involves two small loans made at the same simple interest rate but with different principals and durations. The total interest earned from both loans is known, and the objective is to find the common annual interest rate. It is another example of combining multiple simple interest calculations into one equation with a single unknown rate. Given Data / Assumptions: - Loan 1: principal P1 = Rs 400, time T1 = 3 years. - Loan 2: principal P2 = Rs 500, time T2 = 4 years. - Rate of simple interest R percent per annum is the same for both loans. - Total simple interest from both loans SI total = Rs 160. - Interest is calculated using the simple interest formula, without compounding. Concept / Approach: Simple interest on each loan is SI1 = (P1 * R * T1) / 100 and SI2 = (P2 * R * T2) / 100. The sum SI1 + SI2 equals the total interest of Rs 160. By factoring R and using SI total = (R / 100) * (P1 * T1 + P2 * T2), we can solve for R. This method is efficient because it reduces the two separate equations to one combined expression. Step-by-Step Solution: Step 1: Write SI total = (P1 * R * T1) / 100 + (P2 * R * T2) / 100. Step 2: Factor R / 100 to get SI total = (R / 100) * (P1 * T1 + P2 * T2). Step 3: Compute P1 * T1 = 400 * 3 = 1,200. Step 4: Compute P2 * T2 = 500 * 4 = 2,000. Step 5: Sum them: P1 * T1 + P2 * T2 = 1,200 + 2,000 = 3,200. Step 6: Use SI total = 160, so 160 = (R / 100) * 3,200. Step 7: Rearrange to solve for R: R = (160 * 100) / 3,200. Step 8: Compute numerator: 160 * 100 = 16,000. Step 9: Divide: 16,000 / 3,200 = 5. Step 10: Therefore, R = 5 percent per annum. Verification / Alternative check: Verify by computing interest on each loan at 5 percent. For the Rs 400 loan over 3 years, SI1 = (400 * 5 * 3) / 100 = (400 * 15) / 100 = 6,000 / 100 = Rs 60. For the Rs 500 loan over 4 years, SI2 = (500 * 5 * 4) / 100 = (500 * 20) / 100 = 10,000 / 100 = Rs 100. Total interest SI1 + SI2 = 60 + 100 = Rs 160, which matches the given total. Why Other Options Are Wrong: At 7 percent, total interest would be larger than Rs 160. At 9 percent or 10 percent, the interest amounts would be even higher. None of these match the total interest of Rs 160. Only 5 percent per annum produces exactly Rs 160 in combined simple interest. Common Pitfalls: A common mistake is to average the time periods or principals instead of using the weighted sum P1 * T1 + P2 * T2. Some learners also forget to divide by 100 when handling percentages. Writing the combined equation clearly and solving step by step avoids these errors. Final Answer: The simple interest rate per annum is 5% per year.

Question 17

Reena takes a loan of Rs 1,200 at simple interest for as many years as the numerical value of the rate of interest; if she pays Rs 432 as interest at the end of the loan period, what is the annual rate of simple interest in percent?

Accepted Answer

Introduction / Context: This question is almost identical in structure to an earlier problem where the number of years equals the numerical value of the rate of interest. Reena borrows money at simple interest with this special relationship between time and rate, and the total interest paid is known. The goal is to deduce the annual rate, which again involves forming and solving a quadratic relation in R based on the simple interest formula. Given Data / Assumptions: - Principal borrowed P = Rs 1,200. - Total simple interest paid SI = Rs 432. - Let the annual simple interest rate be R percent. - Time period T in years is equal to R, the numerical value of the rate. - Interest is calculated strictly using the simple interest formula. Concept / Approach: The simple interest formula is SI = (P * R * T) / 100. The condition T = R leads to SI = (P * R^2) / 100. Substituting P and SI yields an equation in R^2, which we can solve to get R. Because R represents an interest rate, we only consider the positive root. This algebraic step is crucial for correctly interpreting such special condition problems in simple interest. Step-by-Step Solution: Step 1: Start from SI = (P * R * T) / 100. Step 2: Use T = R to get SI = (P * R^2) / 100. Step 3: Substitute SI = 432 and P = 1,200. Step 4: Write the equation: 432 = (1,200 * R^2) / 100. Step 5: Multiply both sides by 100: 432 * 100 = 1,200 * R^2. Step 6: 432 * 100 = 43,200, so 43,200 = 1,200 * R^2. Step 7: Divide both sides by 1,200: R^2 = 43,200 / 1,200 = 36. Step 8: Take the positive square root: R = square root of 36 = 6. Step 9: Therefore, the annual rate of simple interest is 6 percent per annum. Verification / Alternative check: Verify by substituting R = 6 percent and T = 6 years back into the formula. SI = (1,200 * 6 * 6) / 100. First 1,200 * 6 = 7,200, then 7,200 * 6 = 43,200, and dividing by 100 gives SI = Rs 432. This matches the given interest amount exactly, confirming that a 6 percent rate is correct. Why Other Options Are Wrong: A rate of 3.6 percent would require R^2 to be 12.96, which does not satisfy the equation 1,200 * R^2 / 100 = 432. A rate of 18 percent gives R^2 = 324, resulting in an interest much larger than Rs 432. The option stating that the rate cannot be determined is incorrect because we obtained a unique positive solution. Only 6 percent satisfies the given conditions. Common Pitfalls: Learners sometimes forget that T equals R, and instead treat T as an independent value. Others may incorrectly handle the percent conversion or miscalculate R^2. Recognising that the condition T = R transforms the simple interest formula into a quadratic in R is the key to solving this smoothly. Final Answer: The annual rate of simple interest for Reena's loan is 6% per annum.

Question 18

Jan invests $210 in a fixed deposit account with a building society that pays 8% simple interest per annum for a period of 18 months; how much money in total does she receive at the end of the 18 months?

Accepted Answer

Introduction / Context: This question is a direct application of the simple interest formula with time expressed in months rather than years. Jan invests a small amount at a fixed annual rate and the deposit runs for 18 months. The goal is to compute the total amount received, which is the sum of the original principal and the simple interest earned over that period. Given Data / Assumptions: - Principal P = 210 dollars. - Annual simple interest rate R = 8 percent per annum. - Time period is 18 months. - Interest is calculated using simple interest, not compound interest. - Required quantity is total amount A = principal + interest. Concept / Approach: The simple interest formula SI = (P * R * T) / 100 requires time T in years. Therefore, we first convert 18 months into years. Since 12 months equal 1 year, 18 months equals 18 / 12 = 1.5 years. After converting time, we compute the simple interest, then add it to the principal to obtain the total maturity amount for Jan's deposit. Step-by-Step Solution: Step 1: Convert 18 months to years: T = 18 / 12 = 1.5 years. Step 2: Identify P = 210 dollars, R = 8 percent, T = 1.5 years. Step 3: Use SI = (P * R * T) / 100. Step 4: Substitute values: SI = (210 * 8 * 1.5) / 100. Step 5: Compute 210 * 8 = 1,680. Step 6: Multiply 1,680 by 1.5 to get 2,520. Step 7: Divide by 100: SI = 2,520 / 100 = 25.20 dollars. Step 8: Compute total amount A = P + SI = 210 + 25.20 = 235.20 dollars. Step 9: Therefore, Jan receives 235.20 dollars at the end of 18 months. Verification / Alternative check: We can think of the annual interest first. For one year, interest is (210 * 8 * 1) / 100 = 16.80 dollars. For half a year (0.5 year), interest is half of that, 8.40 dollars. Summing 16.80 and 8.40 gives 25.20 dollars of total interest in 1.5 years. Adding this to the principal 210 dollars again gives 235.20 dollars, confirming the result. Why Other Options Are Wrong: An amount of 434.00 dollars is far larger than possible from such a small principal and rate in only 18 months. An amount of 345.00 dollars also overstates the interest significantly. A total of 233.20 dollars would imply interest of only 23.20 dollars, which does not match the 8 percent rate over 1.5 years. Only 235.20 dollars corresponds to the correct simple interest calculation. Common Pitfalls: Learners sometimes forget to convert months to years and instead use T = 18 directly, which hugely overestimates interest. Another mistake is to treat 18 months as 1.8 years instead of 1.5 years. Careful handling of unit conversions for time is crucial when applying interest formulas correctly. Final Answer: At the end of 18 months, Jan receives a total of $235.20.

Question 19

An amount of $720 is invested for 36 months and earns $205.20 in simple interest; what is the corresponding yearly simple interest rate in percent per annum for this investment?

Accepted Answer

Introduction / Context: This question gives the principal, the total simple interest earned, and the time expressed in months. The task is to determine the annual simple interest rate. It is a practical problem similar to real fixed deposit or savings account calculations, and it tests conversion of months to years and correct use of the simple interest formula for rate. Given Data / Assumptions: - Principal P = 720 dollars. - Simple interest SI = 205.20 dollars. - Time period = 36 months. - Rate of simple interest R percent per annum is unknown. - Interest is calculated according to the simple interest formula. Concept / Approach: First convert time from months to years because the rate is per annum. Since 12 months equal 1 year, 36 months correspond to 36 / 12 = 3 years. Then apply SI = (P * R * T) / 100 and rearrange to R = (SI * 100) / (P * T). Substituting the values of SI, P, and T gives the annual rate in percent per annum. Step-by-Step Solution: Step 1: Convert 36 months to years: T = 36 / 12 = 3 years. Step 2: Identify P = 720 dollars, SI = 205.20 dollars, T = 3 years. Step 3: Use the formula SI = (P * R * T) / 100. Step 4: Rearrange for R: R = (SI * 100) / (P * T). Step 5: Substitute SI = 205.20, P = 720, T = 3. Step 6: Compute denominator P * T = 720 * 3 = 2,160. Step 7: Compute numerator SI * 100 = 205.20 * 100 = 20,520. Step 8: Divide: R = 20,520 / 2,160. Step 9: Calculate 20,520 / 2,160 = 9.5. Step 10: Therefore, the annual simple interest rate is 9.5 percent per annum. Verification / Alternative check: Verify by recalculating SI with R = 9.5 percent and T = 3 years. SI = (720 * 9.5 * 3) / 100. First 720 * 9.5 = 6,840, then multiply by 3 to get 20,520, and divide by 100 to get 205.20 dollars of interest. This matches the given interest amount, confirming that the rate of 9.5 percent is correct. Why Other Options Are Wrong: A rate of 7.5 percent would give SI = (720 * 7.5 * 3) / 100 = 162 dollars, which is too small. At 8.5 percent, SI is 183.60 dollars, still less than 205.20. At 10.5 percent, SI becomes 226.80 dollars, which is too large. Only 9.5 percent produces exactly 205.20 dollars of interest over 3 years on a principal of 720 dollars. Common Pitfalls: Some learners forget to convert months to years and incorrectly set T = 36, which leads to an extremely small and unrealistic rate. Others may misplace the principal and interest in the rate formula. Carefully converting time units and writing R = SI * 100 / (P * T) helps avoid these errors. Final Answer: The yearly simple interest rate is 9.5% per annum.

Question 20

A loan of $15,000 is taken out at 7% simple interest per annum and is to be repaid in full after 7 months; under simple interest, what interest is due and what total amount must be repaid at the end of 7 months?

Accepted Answer

Introduction / Context: This loan question uses simple interest with time expressed in months. The borrower takes a loan of 15,000 dollars at a fixed annual interest rate and repays it after 7 months. The problem asks both for the interest due and the total repayment amount. It tests correct handling of time conversion and application of the simple interest formula to short term loans. Given Data / Assumptions: - Principal P = 15,000 dollars. - Annual simple interest rate R = 7 percent per annum. - Time = 7 months. - Simple interest is used; no compounding is mentioned. - Required quantities: interest due and total amount to be repaid. Concept / Approach: The simple interest formula SI = (P * R * T) / 100 requires T in years. Hence 7 months must be converted to years as 7 / 12 years. Once we have T in years, we compute SI, then add it to the principal to find the total amount repayable. The answer options show only total amounts, but we can easily report both interest and amount in the explanation. Step-by-Step Solution: Step 1: Convert 7 months to years: T = 7 / 12 years. Step 2: Identify P = 15,000 dollars, R = 7 percent, T = 7 / 12. Step 3: Use SI = (P * R * T) / 100. Step 4: Substitute: SI = (15,000 * 7 * (7 / 12)) / 100. Step 5: Compute 15,000 * 7 = 1,05,000. Step 6: Multiply by 7 to get 1,05,000 * 7 = 7,35,000. Step 7: Divide by 12: 7,35,000 / 12 = 61,250. Step 8: Divide by 100: SI = 61,250 / 100 = 612.50 dollars. Step 9: Compute total amount A = P + SI = 15,000 + 612.50 = 15,612.50 dollars. Verification / Alternative check: We can also find the interest per year first. For one full year, interest is (15,000 * 7 * 1) / 100 = 1,050 dollars. For 7 months, which is 7 / 12 of a year, interest is 1,050 * 7 / 12 = 1,050 * 0.5833, which is approximately 612.50 dollars. Adding this to the principal gives a total repayment of 15,612.50 dollars, confirming the calculation. Why Other Options Are Wrong: An amount of 14,612.50 dollars would imply negative interest, which is impossible at a positive rate. An amount of 13,612.50 dollars is even lower and does not reflect any interest at all. An amount of 17,612.50 dollars assumes far more interest than 7 percent for 7 months on 15,000 dollars. Only 15,612.50 dollars is consistent with the simple interest formula and given data. Common Pitfalls: Learners often forget to convert months to years and use T = 7 in the formula, leading to a grossly inflated interest. Another mistake is to miscalculate the fraction 7 / 12 or to round too early. Keeping the exact fraction until the final step yields the correct interest and total amount. Final Answer: The interest due is 612.50 dollars, and the total amount to be repaid is $15,612.50.

Simple Interest Questions