Quantitative Aptitude

Simple and Compound Interest

3,394 Questions
All Simple interest and its inverse forms 768 Compound interest with annual compounding 742 Simple-interest growth and split sums 626 Difference between compound and simple interest 479 Half-yearly and quarterly compounding 252 Changing rates and fractional years 201 Installments (CI based) 190 Ratio of principal to interest 118 Population growth and depreciation 16

Simple and Compound Interest Questions

Multiple choice

The difference between the simple interest and compound interest with interest being compounded annually, on a certain sum at 20% per annum for 3 years is Rs.1152. Find the sum. एक निश्चित धनराशि पर 20% वार्षिक ब्याज की दर से 3 वर्ष में साधारण ब्याज और चक्रवृद्धि ब्याज में अन्तर 1152 रु. है जबकि ब्याज वार्षिक रूप से उपचयित होता है | धनराशि ज्ञात कीजिये |

  1. Rs./रु.9500

  2. Rs./रु.10000

  3. Rs./रु.9000

  4. Rs./रु.8000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For 3 years at 20%, simple interest = 0.6P and compound interest = 0.728P. The difference is 0.728P - 0.6P = 0.128P. Given the difference is Rs.1152, we solve 0.128P = 1152, giving P = Rs.9000. The difference arises because compound interest earns interest on accumulated interest, while simple interest only earns on the principal.

Multiple choice

What is the compound interest on Rs. 1600 at 25% per annum for 2 years compounded annually? 1600 रू. का 25% वार्षिक दर से प्रतिवर्ष संयोजित करने पर 2 वर्ष के लिये चक्रवृद्धि ब्याज क्या है?

  1. Rs. 700

  2. Rs. 750

  3. Rs. 800

  4. Rs. 900
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Amount after 2 years = 1600(1 + 25/100)² = 1600 × (1.25)² = 1600 × 1.5625 = 2500. Compound Interest = Amount - Principal = 2500 - 1600 = 900.

Multiple choice

Dinesh invested certain amounts in two different banks PNB and SBI. PNB offers simple interest at 14% per annum and SBI offers compound interest at 5% per annum. The interest accrued on the amount invested in PNB in 2 years was Rs.4200 and the total amount invested was Rs.38000. What was the interest accrued on the amount invested in SBI?

  1. Rs.4375.5

  2. Rs.2857.5

  3. Rs.2357.5

  4. Rs.2537.5

  5. Can't be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

PNB investment: SI = P×R×T/100, so 4200 = P×14×2/100, giving P = 4200×100/28 = Rs.15,000. SBI investment = Rs.38,000 - Rs.15,000 = Rs.23,000. CI for 2 years at 5%: Amount = 23,000×(1.05)² = 23,000×1.1025 = Rs.25,357.50. Interest = Rs.25,357.50 - Rs.23,000 = Rs.2,357.50. Option C is correct.

Multiple choice

What is the difference between simple interest and compound interest on a sum of Rs. 9000 at 20% per annum for 3 years 9000 रू. की धनराशि पर 3 वर्ष में 20% वार्षिक ब्याज की दर से साधारण ब्याज और चक्रवृद्धि ब्याज में क्या अन्तर है?

  1. 1125

  2. 1251

  3. 1215

  4. 1152
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple Interest = P × R × T / 100 = 9000 × 20 × 3 / 100 = Rs. 5400. Compound Interest = P[(1 + R/100)^T - 1] = 9000[(1.2)³ - 1] = 9000(1.728 - 1) = 9000(0.728) = Rs. 6552. Difference = CI - SI = 6552 - 5400 = Rs. 1152. This matches option D.

Multiple choice

A sum of money with compound interest amounts to Rs. 133100 in 3 years and Rs. 161051 in 5 years. What is the rate of compound interest per annum?

  1. 7%

  2. 10%

  3. 13%

  4. 15%

  5. 17%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In compound interest, amount = P(1 + r/100)^n. For year 3: P(1+r/100)^3 = 133100. For year 5: P(1+r/100)^5 = 161051. Dividing gives (1+r/100)^2 = 161051/133100 = 1.21. Taking square root: 1+r/100 = 1.1, so r = 10%. Check: if P = 100000 and r = 10%, then year 3 = 100000 × 1.331 = 133100 ✓ and year 5 = 100000 × 1.61051 = 161051 ✓

Multiple choice

Maneesh invests some money in three different schemes for 4 years, 8 years and 12 years at 10%, 15% and 20% Simple Interest respectively. At the completion of each scheme, he gets the same interest. The ratio of his investments is

  1. 6 : 2 : 1

  2. 5 : 2 : 1

  3. 5 : 2 : 3

  4. 5 : 2 : 7

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For Simple Interest, I = P × R × T ÷ 100. Since interest is equal: P1 × 10 × 4 = P2 × 15 × 8 = P3 × 20 × 12. This gives: 40P1 = 120P2 = 240P3. Dividing by 40: P1 = 3P2 = 6P3. So P1 : P2 : P3 = 6 : 2 : 1, which matches option A.

Multiple choice

Sakshi borrows Rs.7000 at simple Interest from Tanshika. At the end of 3 years, she again borrows Rs.3000 and settled that amount after paying Rs.4615 as interest after 8 years from the time she made the first borrowing. What is the rate of interest?

  1. 5.5%

  2. 6.5%

  3. 7.5%

  4. 9.5%

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let r be the annual rate. First borrowing: Rs.7000 for 8 years gives interest = 7000 × r × 8 = 56000r. Second borrowing: Rs.3000 for 5 years (from year 3 to year 8) gives interest = 3000 × r × 5 = 15000r. Total interest = 56000r + 15000r = 71000r. Given 71000r = 4615, so r = 4615/71000 = 0.065 = 6.5%.

Multiple choice

A sum at certain rate of compound interest become 600 in 8 years and become 900 at the end of 16 years. Find the amount after 20 years? एक राशि एक निश्चित चक्रवृद्धि ब्याज की दर से 8 वर्षों में 600 तथा 16 वर्षों में 900 हो जाती है। 20 वर्षों के पश्चात मिश्रधन ज्ञात कीजिये ?

  1. Rs. 1625

  2. Rs. 1225

  3. Rs. 1125

  4. Rs. 5625
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be principal and rate be r%. From the data: P(1+r)^8 = 600 and P(1+r)^16 = 900. Dividing gives (1+r)^8 = 3/2. So P = 600/(3/2) = 400. Amount after 20 years = 400 × (3/2)^(20/8) = 400 × (3/2)^2.5 ≈ 1125 (closest option). The calculation involves fractional exponents which are approximated in exam settings.

Multiple choice

Find the ratio of compound interest of certain sum for 2 year compounded half yearly to the simple interest for 3 year of same principal. If rate of interest is 20% per annum. किसी निश्चित मूलधन का 2 वर्षो का चक्रवृद्धि ब्याज जो अर्धवार्षिक संयोजित होता है तथा उसी धन पर 3 वर्षो के साधारण ब्याज का अनुपात अनुपात बताईये। यदि ब्याज दर 20% प्रति वर्ष है।

  1. 1541 : 6000

  2. 2000 : 1547

  3. 1547 : 2000

  4. 12.32 : 10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

CI for 2 years compounded half-yearly: rate per half-year = 10%, periods = 4. Amount = P(1 + 0.1)⁴ = P × 1.4641, so CI = 0.4641P. SI for 3 years at 20%: SI = P×3×0.2 = 0.6P. Ratio CI:SI = 0.4641:0.6 = 4641:6000 = 1547:2000.

Multiple choice

The C.I. after 3 year on certain sum Rs. 136.5 more than the C.I. of Ist year if rate of compound interest is 16 2 3 % then find the sum of money ?

  1. 356

  2. 324

  3. 376

  4. 249

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rate = 16 2/3% = 1/6. CI for 3 years on P: P[(1 + 1/6)³ - 1] = P(7/216) = 7P/216 ≈ 0.0324P. CI for 1st year: P/6 ≈ 0.1667P. Difference = 7P/216 - 36P/216 = -29P/216 = 136.5. Solving: P = 324. Option B is correct. Option D (249) is close but incorrect.

Multiple choice

The simple interest accrued on a certain sum is Rs.40761 in 9 years at the rate of 7 p.c.p.a. What would be the compund interest accrued on that sum at the rate of 5 p.c.p.a. in 2 years?

  1. Rs.7631.75

  2. Rs.6613.75

  3. Rs.6631.75

  4. Rs.6630.75

  5. Rs.6836.75
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

SI = Rs.40761 for 9 years @ 7%. Principal = 40761×100/(9×7) = Rs.64683.43. CI for 2 years @ 5% = 64683.43×[(1.05)²-1] = 64683.43×0.1025 = Rs.6631.75. Option A has misplaced decimal (7631.75), B and D have wrong digits (6613.75, 6630.75), E has wrong hundreds.

Multiple choice

With compound interest, a certain sum of money become 9 times in 36 years, In how many years it will become 243 times at the same rate of interest?

  1. 72

  2. 54

  3. 108

  4. 90

  5. None of these.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In compound interest, (1+r)^t = amount ratio. Given (1+r)^36 = 9. We need t for (1+r)^t = 243. Notice 9 = 3² and 243 = 3^5. So (1+r)^36 = 3² → 1+r = 3^(2/36) = 3^(1/18). For 243 = 3^5: (3^(1/18))^t = 3^5 → t/18 = 5 → t = 90 years. Option D is correct. Option A (72) assumes doubling pattern, which doesn't apply here.