Question 1

Find the difference between the simple interest and the compound interest on Rs. 1200 for 1 year at 10% per annum, when interest is reckoned half-yearly.

Accepted Answer

Problem restatement Compare CI (compounded half-yearly) and SI for 1 year at the same nominal rate (10%) on Rs. 1200; report CI − SI. Given data P = Rs. 1200 Nominal rate = 10% p.a.; half-yearly compounding ⇒ 5% per half-year Time = 1 year = 2 half-years Concept/Approach Compute CI via amount factor (1 + r÷m)m for m = 2. Compute SI via P × r × t. Take the difference. Step-by-step calculation Amount (CI) = 1200 × (1 + 0.05)2 = 1200 × 1.1025 = 1323.00CI = 1323.00 − 1200 = Rs. 123.00SI = P × r × t = 1200 × 0.10 × 1 = Rs. 120.00Difference = 123.00 − 120.00 = Rs. 3 Common pitfalls Using 0.4 hour–type conversions here is irrelevant; the compounding frequency is semi-annual: use 5% twice.

Question 2

If the simple interest on a sum for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same principal, at the same rate, for the same 2 years?

Accepted Answer

Problem restatement From SI over 2 years, infer the principal, then compute CI for the same period at the same rate. Given data SI = Rs. 50 on rate r = 5% p.a., time t = 2 years Concept/Approach Use SI = P r t to get P. Then CI = P[(1 + r)t − 1]. Step-by-step calculation 50 = P × 0.05 × 2 ⇒ 50 = 0.10P ⇒ P = Rs. 500CI = 500 × [(1.05)2 − 1] = 500 × (1.1025 − 1) = 500 × 0.1025CI = Rs. 51.25 Verification/Alternative Year-wise: Year 1 interest = 25; Year 2 interest = 25 on P plus 1.25 on previous year's interest = 26.25; total = 51.25. Common pitfalls Forgetting that CI includes interest on interest in the second year.

Question 3

Albert invests Rs. 8000 at 5% p.a. compounded annually for 2 years. What is the maturity amount?

Accepted Answer

Problem restatement Compute the amount after 2 years at 5% compound interest on Rs. 8000. Given data P = Rs. 8000, r = 5% p.a., t = 2 years Concept/Approach Use the compound amount formula A = P(1 + r)t. Step-by-step calculation A = 8000 × (1.05)2 = 8000 × 1.1025 = Rs. 8820 Verification/Alternative Year 1: interest = 400 ⇒ amount = 8400; Year 2: interest = 420 ⇒ amount = 8820.

Question 4

Find the effective annual rate corresponding to a nominal 6% per annum payable half-yearly.

Accepted Answer

Problem restatement Convert a nominal 6% p.a. with semi-annual compounding into an effective annual rate. Given data Nominal rate = 6% p.a., compounding m = 2 times per year Concept/Approach Effective rate reff = (1 + r÷m)m − 1. Step-by-step calculation reff = (1 + 0.06÷2)2 − 1 = (1.03)2 − 1 = 1.0609 − 1 = 0.0609 = 6.09% p.a. Common pitfalls Multiplying 6% by 2% directly is wrong; compounding must be applied.

Question 5

What is the compound interest on Rs. 25,000 for 3 years at 12% p.a. compounded annually?

Accepted Answer

Problem restatement Compute CI for 3 years at 12% on Rs. 25,000. Given data P = Rs. 25,000; r = 12% p.a.; t = 3 years Concept/Approach Amount A = P(1 + r)t; CI = A − P. Step-by-step calculation A = 25,000 × (1.12)3 = 25,000 × 1.404928 = 35,123.20CI = 35,123.20 − 25,000 = Rs. 10,123.20 Verification/Alternative Year-wise interest: 3,000; then 3,360; then 3,763.20 ⇒ total 10,123.20. Common pitfalls Adding 12% thrice to principal (simple interest) underestimates the final amount; compounding is required.

Question 6

The compound interest on a sum for 2 years at 10% p.a. is Rs. 525. What is the simple interest on the same sum for double the time at half the rate per annum?

Accepted Answer

Problem restatement Given CI over 2 years at 10% is Rs. 525. Find SI for 4 years at 5% on the same principal. Given data CI (2 years, 10%) = Rs. 525 Target: SI (4 years, 5%) on same P Concept/Approach From CI = P[(1 + 0.10)2 − 1] = 0.21P, infer P. Then apply SI = P r t. Step-by-step calculation 0.21P = 525 ⇒ P = 525 ÷ 0.21 = Rs. 2500SI = 2500 × 0.05 × 4 = Rs. 500 Verification/Alternative Direct CI check: (1.1)2 − 1 = 0.21; 0.21 × 2500 = 525 (consistent).

Question 7

At what annual rate of compound interest will Rs. 1200 amount to Rs. 1348.32 in 2 years?

Accepted Answer

Problem restatement Find r such that 1200(1 + r)2 = 1348.32. Given data P = 1200; A = 1348.32; t = 2 years Concept/Approach Solve for r from (1 + r)2 = A÷P. Step-by-step calculation (1 + r)2 = 1348.32 ÷ 1200 = 1.12361 + r = √1.1236 = 1.06r = 0.06 = 6% p.a. Common pitfalls Taking r = 12.36% (the two-year growth) without extracting the square root.

Question 8

Find the difference between the compound interests on Rs. 5000 for 1½ years at 4% p.a. when interest is compounded (i) yearly and (ii) half-yearly.

Accepted Answer

Problem restatement Compute CI for 1½ years at 4% p.a. under two regimes: annual compounding vs half-yearly compounding. Report the difference (half-yearly minus yearly). Given data P = Rs. 5000 r = 4% p.a. Time = 1.5 years Concept/Approach (i) Compounded yearly: 1 full year compounded, then simple interest for the remaining half-year on the amount after 1 year. (ii) Compounded half-yearly: 3 half-year periods at 2% each. Step-by-step calculation (i) Yearly: Amount = P × 1.04 × (1 + 0.04 × 0.5) = P × 1.04 × 1.02 = P × 1.0608(ii) Half-yearly: Amount = P × (1.02)3 = P × 1.061208Difference in amount = P(1.061208 − 1.0608) = P × 0.000408With P = 5000: Difference = 5000 × 0.000408 = Rs. 2.04 Verification/Alternative Compute each amount numerically: Yearly = 5000 × 1.0608 = 5304.00; Half-yearly = 5000 × 1.061208 = 5306.04; Difference = 2.04. Common pitfalls Applying annual compounding for 1.5 years as 1.041.5 (not standard in yearly compounding) or ignoring the half-year SI treatment.

Question 9

A bank offers 5% compound interest calculated half-yearly. A customer deposits Rs. 1600 on 1 January and another Rs. 1600 on 1 July of the same year. What is the total interest earned by 31 December of that year?

Accepted Answer

Problem restatement Interest is compounded twice a year at 5% p.a. (i.e., 2.5% per half-year). Two equal deposits are made: one on 1 Jan (earns two half-years), and one on 1 Jul (earns one half-year). Find the total interest by year end. Given data Rate per half-year = 5% ÷ 2 = 2.5% = 0.025 Deposit 1: Rs. 1600 on 1 Jan → 2 half-years Deposit 2: Rs. 1600 on 1 Jul → 1 half-year Concept/Approach Treat each deposit as a separate principal for its own compounding duration and then sum the interests. Step-by-step calculation Interest on 1st deposit = 1600[(1 + 0.025)2 − 1]= 1600(1.050625 − 1) = 1600 × 0.050625 = 81.00Interest on 2nd deposit = 1600[(1 + 0.025) − 1] = 1600 × 0.025 = 40.00Total interest = 81.00 + 40.00 = Rs. 121 Verification/Alternative Amount of 1st deposit at year end = 1600 × 1.050625 = 1681.00 (so interest 81.00). Amount of 2nd deposit = 1600 × 1.025 = 1640.00 (so interest 40.00). Sum of interests = 121.00. Common pitfalls Applying 5% for the July deposit (should be 2.5% for one half-year), or compounding both deposits for two periods. Final Answer Rs. 121

Question 10

What is the least number of complete years for a sum to more than double at 20% compound interest per annum?

Accepted Answer

Problem restatement Find the smallest integer n such that (1 + 0.20)n > 2. Given data Annual compound rate r = 20% = 0.20 Target: amount factor > 2 Concept/Approach Test integer years until the compound factor exceeds 2. Step-by-step calculation (1.2)3 = 1.728 < 2(1.2)4 = 2.0736 > 2Least n = 4 Verification/Alternative Using logs: n > log 2 ÷ log 1.2 ≈ 0.3010 ÷ 0.07918 ≈ 3.80 → next integer 4. Common pitfalls Comparing to 2.0 after only 3 years (still short). Final Answer 4 years

Question 11

An amount increases by 60% in 6 years at simple interest. What is the compound interest on Rs. 12,000 for 3 years at the same annual rate?

Accepted Answer

Problem restatement First extract the annual simple-interest rate from a 60% increase over 6 years, then apply that rate for 3 years with annual compounding on Rs. 12,000. Given data SI increase over 6 years = 60% ⇒ r × 6 = 0.60 ⇒ r = 0.10 = 10% p.a. Principal for CI = Rs. 12,000; time = 3 years Concept/Approach Use SI to find r, then compute CI via the amount factor (1 + r)t. Step-by-step calculation A = 12,000 × (1.10)3 = 12,000 × 1.331 = 15,972CI = A − P = 15,972 − 12,000 = Rs. 3,972 Verification/Alternative Year-wise interest: 1200; then 1320; then 1452 → total 3972. Common pitfalls Confusing SI and CI; using 60% over 3 years (it was over 6 years). Final Answer Rs. 3,972

Question 12

The compound interest on Rs. 30,000 at 7% per annum is Rs. 4,347. Find the period (in years).

Accepted Answer

Problem restatement Given CI and rate, determine t such that P[(1 + r)t − 1] = CI. Given data P = 30,000; r = 7% = 0.07 CI = 4,347 ⇒ (1 + r)t − 1 = 4,347 ÷ 30,000 = 0.1449 Concept/Approach Recognize the square of 1.07: (1.07)2 = 1.1449. Step-by-step calculation (1.07)t = 1 + 0.1449 = 1.1449Since (1.07)2 = 1.1449, we have t = 2 years Verification/Alternative Compute CI directly: 30,000[(1.07)2 − 1] = 30,000(0.1449) = 4,347. Common pitfalls Taking t = 1 (would give only 7%, not 14.49%). Final Answer 2 years

Question 13

The difference between compound and simple interest on Rs. 15,000 for 2 years is Rs. 96. What is the annual rate of interest?

Accepted Answer

Problem restatement For 2 years at rate r, CI − SI = P r2. Use this identity to solve for r. Given data P = 15,000; CI − SI = 96 Concept/Approach For two years, CI = P(2r + r2) and SI = P(2r); their difference is P r2. Step-by-step calculation P r2 = 96 ⇒ 15,000 r2 = 96r2 = 96 ÷ 15,000 = 0.0064r = √0.0064 = 0.08 = 8% p.a. Common pitfalls Using 96 as one year difference (the identity holds specifically for 2 years). Final Answer 8% p.a.

Question 14

Simple interest on a sum for 3 years at 8% p.a. equals half the compound interest on Rs. 4,000 for 2 years at 10% p.a. Find the sum placed at simple interest.

Accepted Answer

Problem restatement Compute CI on Rs. 4,000 for 2 years at 10%, halve it, and set equal to SI on unknown principal at 8% for 3 years. Given data CI (4,000; 10%; 2 years) = 4,000[(1.10)2 − 1] = 4,000(0.21) = 840 Half of that = 420 SI = P × 0.08 × 3 = 0.24P Step-by-step calculation 0.24P = 420P = 420 ÷ 0.24 = Rs. 1,750 Verification/Alternative Check: SI = 1,750 × 0.24 = 420, which is indeed half of 840. Common pitfalls Using 10% of 4,000 twice without compounding (that would be SI, not CI). Final Answer Rs. 1,750

Question 15

The difference between simple and compound interest compounded annually on a certain sum for 2 years at 4% p.a. is Re. 1. Find the sum.

Accepted Answer

Problem restatement For two years at rate r, the excess of CI over SI equals P r2. Use this to get P. Given data r = 4% = 0.04; CI − SI = Re. 1 Step-by-step calculation P r2 = 1 ⇒ P × (0.04)2 = 1P × 0.0016 = 1 ⇒ P = 625 Verification/Alternative With P = 625: SI (2 yrs) = 625 × 0.08 = 50; CI = 625[(1.04)2 − 1] = 625(0.0816) = 51; difference = 1. Common pitfalls Applying the identity for periods other than exactly 2 years. Final Answer Rs. 625

Question 16

The difference between the compound interest and the simple interest on a certain sum at 5% per annum for 2 years is Rs. 1.50. The sum is?

Accepted Answer

Let the sum be Rs . 100 then S.I. = Rs.(100 x 5 x 2/100)= Rs. 10 C.I = Rs. [{100 x (1 + 5/100)2} - 100] = Rs. 41/4 ∴ Difference between C.I and S.I = Rs. (41/4 - 10) = Re. 0.25 ⇒ 0.25 : 150 : : 100 : P ∴ P = (1.50 x 100) / 0.25 = Rs. 600

Question 17

If the compound interest on a certain sum for 2 years at 12.5% per annum is 170, the simple interest is?

Accepted Answer

Let the principle is P so compound interest = p x ( 1 + (12.5/100))sup>2 - p = 170 ⇒ p x (112.5/100) x (112.5/100) - p = 170 ⇒ P [ 12656.25 - 10000 ] = 170 x 10000 ∴ p = (170 x 10000) / 2656.25 Simple interest SI = (P x T x R )/100 = [{(170 x 10000) / 2656.25} x 2 x 12.5] / 100 = 160

Question 18

A sum amounts to Rs. 1352 in 2 years at 4% compound interest.The sum is?

Accepted Answer

Let the sum be P. Then, 1352 = P(1 +4/100)2 ⇒ 1352 = P x 26/25 x 26/25 ⇒ P = (1352 x 25 x 25) / (26 x 26) = 1250 ∴ Principal = Rs. 1250

Question 19

Rs. 800 at 5% per annum compound interest will amount to Rs. 882 in?

Accepted Answer

Let time be t years ∵ 882 = 800( 1 +5/1000)t ⇒ 882/800 = (21/20)t ⇒ (21/20)2 = (21/20)t ⇒ t =2 ∴ Time = 2years

Question 20

The compound interest on Rs. 2800 for 1 1/ 2 years at 10% per annum is?

Accepted Answer

∵ Final Amount = Rs.[2800 x (1 + 10/100) x (1 +5/100)] = Rs. [ 2800 x 11/10 x 21/20 ] = Rs. 3234 ∴ Required C.I. = Rs.(3234 - 2800) = Rs .434

Compound Interest Questions