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 ratio of difference between simple interest and compound interest of a certain sum of money for 2 years and for 3 years is 5: 16. Then rate of interest is एक निश्चित धनराशि पर 2 वर्ष तथा 3 वर्ष के साधारण ब्याज और चक्रवृद्धि ब्याज के अन्तर में अनुपात 5: 16 है | ब्याज की दर है

  1. 12%

  2. 15%

  3. 25%

  4. 20%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For amount P at rate r%, CI for n years = P[(1+r/100)ⁿ - 1], SI = P × n × r/100. Difference for 2 years: P[(1+r/100)² - 1 - 2r/100] = P(r²/10000). Difference for 3 years: P[(1+r/100)³ - 1 - 3r/100]. Given ratio of differences = 5:16. After simplification, we get r²/10000 : (r²/10000)(3+r/100) = 5:16. So (3+r/100) = 16/5, giving r/100 = 1/5, r = 20%.

Multiple choice

A sum of money put out at compound interest amounts in one year to Rs.4050 and in three years to Rs.4723.92. Find the original sum?

  1. Rs.4000

  2. Rs.5000

  3. Rs.6750

  4. Rs.3750
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P = principal, r = annual rate. After 1 year: P(1+r) = 4050. After 3 years: P(1+r)^3 = 4723.92. Dividing: (1+r)^2 = 4723.92/4050 = 1.1664, so 1+r = 1.08 (r = 8%). Then P = 4050/1.08 = Rs.3750. This uses compound interest formula A = P(1+r)^t.

Multiple choice

If a certain sum of money at simple interest amounts to Rs.5184 in 2 years and Rs.5832 in 3 years, what is the sum?

  1. Rs.3888

  2. Rs.4666

  3. Rs.5444

  4. Rs.6888
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In simple interest, the amount increases by the same interest each year. Interest for 1 year = Rs.5832 - Rs.5184 = Rs.648. Since 2 years amount is Rs.5184, principal + 2 years interest = 5184. So P + 2(648) = 5184, giving P = Rs.3888. This uses the constant annual interest property.

Multiple choice

Simple interest on a certain sum of money for 3 years at 24% per annum is equal to compound interest on Rs. 18000 for 2 years at 20% per annum. The sum placed on simple interest is- 24% प्रतिवर्ष पर 3 वर्ष के लिए किसी धन की एक निश्चित राशि पर साधारण ब्याज, 18000 रूपये पर 20% प्रतिवर्ष की दर से 2 वर्ष के लिए चक्रवृद्धि ब्याज के बराबर है। साधारण ब्याज पर रखी गयी धनराशि है-

  1. Rs./रु. 11000

  2. Rs./रु. 18500

  3. Rs./रु. 15000

  4. Rs./रु. 16200
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Calculate compound interest on Rs 18000 for 2 years at 20%: CI = 18000(1.20² - 1) = 18000 × 0.44 = 7920. Simple interest for 3 years at 24%: SI = P × 0.24 × 3 = 0.72P. Equating: 0.72P = 7920, so P = 11000. The sum placed on simple interest is Rs 11000.

Multiple choice

If the difference between the simple interest and compound interest on a certain sum of money at 10% annual rate of interest in 3 years is Rs.93. Find the sum.

  1. Rs.3000

  2. Rs.9000

  3. Rs.8000

  4. Rs.5000

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

For the difference between CI and SI for 3 years at rate r%: CI - SI = P×(r/100)²×(300+r)/100. Given r=10%, CI-SI=93: 93 = P×(10/100)²×(310)/100 = P×0.01×3.1 = 0.031P. So P = 93/0.031 = Rs.3000. Alternatively, using the approximation CI-SI≈P×r²×(n-1)/10000 for n years: 93≈P×100×2/10000=P×0.02, so P≈4650. Using exact formula gives P=3000. Option A is correct.

Multiple choice

A person invests Rs.8000 in two types of deposits. Part of it he invests at the rate of 10% per annum at simple interest and the rest on simple interest at the rate of 12% per annum. If he receives Rs.10700 in all after 3 years. How much money did he invest at 12%? एक व्यक्ति 8000 रू. दो तरह के खातों में जमा करता है। इसका एक भाग वह 10% साधारण ब्याज की दर से निवेश करता है और शेष भाग को 12% साधारण ब्याज की दर से निवेश करता है। यदि वह इन सभी से 3 वर्ष के बाद 10700 रू. प्राप्त करता है। 12% पर उसने कितनी धनराशि निवेश की थी?

  1. Rs. 5000

  2. Rs. 4000

  3. Rs. 4400

  4. Rs. 4800
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be amount at 12%. Then (8000-x) is at 10%. After 3 years: (8000-x) + (8000-x)×0.10×3 + x + x×0.12×3 = 10700. Simplifying: (8000-x)(1.3) + x(1.36) = 10700. This gives 10400 - 1.3x + 1.36x = 10700, so 0.06x = 300, giving x = 5000. Verification: 3000 at 10% for 3 years gives 3900, 5000 at 12% for 3 years gives 6800, total = 10700. Options B, C, and D are incorrect.

Multiple choice

The compound interest on a certain sum at 5% for 2 years is Rs.738. What will be the simple interest for that sum at the same rate and for the same period? एक निश्चित धनराशि पर 2 वर्षों में 5% की दर से चक्रवृद्धि ब्याज 738 रू. है। उसी धनराशि के लिए उसी समयावधि और समान ब्याज दर पर साधारण ब्याज क्या होगा ?

  1. Rs. 700

  2. Rs. 720

  3. Rs.740

  4. Rs.750
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For compound interest at 5% for 2 years, CI = P[(1.05)² - 1] = 738, so P = 7200. Simple interest = P × r × t = 7200 × 0.05 × 2 = 720. Option B is correct.

Multiple choice

Find the compound interest on Rs.51200 for 9 months at 15% per annum compounded quarterly. 51200 रूपये पर 15% प्रतिवर्ष पर 9 महीनों के लिए चक्रवृद्धि ब्याज ज्ञात कीजिये यदि ब्याज दर तिमाही देय हो।

  1. Rs.5978.7

  2. Rs.5987.7

  3. Rs.5897.7

  4. Rs.5789.7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Principal = 51200, rate = 15% p.a., time = 9 months = 3 quarters. Quarterly rate = 15/4 = 3.75%. Amount = 51200(1 + 3.75/100)^3 = 51200(1.0375)^3 ≈ 57378.7. Compound Interest = 57378.7 - 51200 = 5978.7.

Multiple choice

The simple interest on a sum of certain principal is Rs.1200 in four years at the rate of 8% per annum. What would be the simple interest accrued on thrice of that principal at the rate of 6% per annum in 3 years? एक निश्चित धनराशि पर चार वर्ष में 8% प्रति वर्ष की दर से 1200 रूपये साधारण ब्याज प्राप्त होता है। 3 वर्षों में 6% प्रति वर्ष की दर से उसी धनराशि के तीन गुने पर साधारण ब्याज क्या होगा?

  1. Rs.2025

  2. Rs.3025

  3. Rs.2250

  4. Rs.2150
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given: SI = 1200, T = 4 years, R = 8%. Principal = (100 × 1200)/(8 × 4) = 3750. New SI on 3×3750 = 11250 at 6% for 3 years: SI = (11250 × 6 × 3)/100 = 2025.

Multiple choice

Rohan borrows Rs.10000 from two money lenders at a rate of 6% per annum and 8% per annum respectively, for a period of 3 years. If the total interest he paid was Rs.1980, find the amount borrowed at the rate of 6% per annum. रोहन 3 वर्ष की अवधि के लिए क्रमशः 6% प्रतिवर्ष और 8% प्रतिवर्ष की दर से दो उधारदाताओं से 10000 रूपये का उधार लेता है। यदि उसके द्वारा भुगतान किया गया कुल ब्याज रू. 1980 था, तो प्रतिवर्ष 6% की दर से उधार ली गई राशि ज्ञात कीजिये।

  1. Rs.3000

  2. Rs.4000

  3. Rs.6000

  4. Rs.7000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let amount at 6% be x, at 8% be (10000-x). Total SI: (x × 6 × 3)/100 + ((10000-x) × 8 × 3)/100 = 1980. Simplifying: 18x + 240000 - 24x = 198000, giving -6x = -42000, x = 7000.

Multiple choice

A sum of Rs. 4000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest. If the annual interest is Rs. 352. The sum lent at 8% is- 4000 रुपए की राशि दो भागों में उधार दी गयी, पहला भाग 8% साधारण ब्याज पर और शेष भाग 10% साधारण ब्याज पर। यदि वार्षिक ब्याज 352 रु. है तो 8 % पर उधार दी गयी राशि है-

  1. 2400 Rs./रुपये

  2. 2000 Rs./रुपये

  3. 2500 Rs./रुपये

  4. 1800 Rs./रुपये
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the sum lent at 8% be x. Then (4000-x) is lent at 10%. Total interest: 0.08x + 0.10(4000-x) = 352. Solving: 0.08x + 400 - 0.10x = 352, so -0.02x = -48, giving x = 2400. Verification: 0.08(2400) + 0.10(1600) = 192 + 160 = 352 ✓

Multiple choice

What is the difference between compound interest and simple interest at the rate of 12% at the end of three years on a sum of Rs. 12000. रू. 12000 की राशि पर 12% की दर पर 3 वर्ष के अन्त में उपचित चक्रवृद्धि ब्याज और साधारण ब्याज के बीच क्या अन्तर है ?

  1. Rs.539.136

  2. Rs.602.242

  3. Rs.495.248

  4. Rs.488.322
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simple Interest = P × R × T / 100 = 12000 × 12 × 3 / 100 = Rs. 4320. Compound Interest = P × (1 + R/100)^T - P = 12000 × (1.12)³ - 12000 ≈ Rs. 4859.136. The difference is Rs. 4859.136 - Rs. 4320 = Rs. 539.136.

Multiple choice

An amount is invested 6% simple interest and another amount double the first one at 10% simple interest. The total interest per annum earned is Rs. 1170. What will be the total interest if the entire amount is invested at 10% एक धनराशि को 6% साधारण ब्याज पर निवेश किया गया और दूसरी धनराशि जोकि पहली का दोगुना है, को 10% साधारण ब्याज पर निवेश किया। प्रतिवर्ष प्राप्त कुल ब्याज 1170 रू. है। कुल ब्याज क्या होगा यदि पूरी धनराशि को 10% पर निवेशित किया जाता है।

  1. Rs.1350

  2. Rs.13500

  3. Rs.4500

  4. Rs. 9000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let first amount = x at 6% SI, second amount = 2x at 10% SI. Total interest per year = x*0.06 + 2x*0.10 = 0.06x + 0.20x = 0.26x = 1170. Therefore, x = 1170/0.26 = 4500. Total amount = x + 2x = 3x = 13500. If entire amount invested at 10%: Interest = 13500 * 0.10 = 1350. Option B (13500) is the total principal, not interest. Option C (4500) is just the first investment. Option D (9000) is 2x, not the interest.

Multiple choice

What is the initial sum borrowed by Rajeev? I. Final sum is increased by Rs.16800 than initial value at the rate of 7% per annum in 5 years when calculated on simple interest. II. Compound interest on sum becomes Rs 7566 at the rate of 5% in 3 years compounded annually. III. Simple interest on the sum at the rate of 5% per annum in 3 years is Rs 366 less than compound interest.

  1. All three together are sufficient

  2. All three together are not sufficient

  3. Only I or II is sufficient

  4. Any one is sufficient

  5. II and either I or III are sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I: SI = P×7×5/100 = 16800, so P = 16800×100/35 = 48000. Statement II: CI = P[(1+5/100)^3-1] = 7566, giving P = 7566/0.157625 ≈ 48000. Statement III: SI(5%,3yr)=0.15P, CI(5%,3yr)=0.157625P, difference=0.007625P=366, giving P=366/0.007625≈48000. Each statement alone is sufficient.

Multiple choice

The difference between simple and compound interest compounded yearly at the rate of 4% in a two year period is Rs. 10. The amount invested is- 4% की दर से वार्षिक रूप से संयोजित होने पर 2 वर्ष के समय के लिए साधारण ब्याज और चक्रवृद्धि ब्याज का अन्तर 10 रू. है। निवेशित की गई धनराशि है-

  1. Rs. 4500

  2. Rs. 5750

  3. Rs. 6000

  4. Rs. 6250
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For 2 years at 4%, let principal = P. Simple Interest = P×4×2/100 = 0.08P. Compound Interest = P×(1.04)² - P = P×1.0816 - P = 0.0816P. Difference = CI - SI = 0.0816P - 0.08P = 0.0016P = Rs. 10. Therefore P = 10/0.0016 = 6250.