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

A sum of Rs. 8400 was taken as a loan. This is to be repaid in two equal installments. If the rate of interest is 10% per annum, compounded annually, then the value of each installment is. रू. 8400 की एक धनराशि उधार पर ली गई है। इसे दो बराबर किस्तों में चुकाया जाना है। यदि चक्रवृद्धि ब्याज की दर 10% प्रति वर्ष है जो वार्षिक रूप से जोड़ा जाता है, तो प्रत्येक किस्त का मान क्या है?

  1. Rs./रू. 4200

  2. Rs./रू. 4480

  3. Rs./रू. 4840

  4. Rs./रू. 4680
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a loan repaid in equal annual installments under compound interest, use the formula: P = x[1 - (1 + r)⁻ⁿ]/r where x is the installment. Here: 8400 = x[1 - (1.1)⁻²]/0.1 = x[1 - 1/1.21]/0.1 = x[0.21/1.21]/0.1 = x(21/121). Solving: x = 8400 × 121/21 = 400 × 121 = 4840. Verification: After year 1, balance = 8400(1.1) - 4840 = 9240 - 4840 = 4400; after year 2: 4400(1.1) - 4840 = 4840 - 4840 = 0. Key distractor: 4680 (uses simple interest approximation).

Multiple choice

The difference between the simple and the compound interest on a certain sum of money at 4% per annum in 3 years is Rs. 30.4. What is the sum? एक धनराशि पर 4% प्रति वर्ष की दर से 3 वर्ष में साधारण व चक्रवृद्धि ब्याज का अन्तर 30.4 रू. है। धनराशि क्या है?

  1. Rs. 5000

  2. Rs. 6000

  3. Rs. 7500

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

For 3 years at r%: CI - SI = P[(1 + r)³ - 1 - 3r] = P[(1.04)³ - 1 - 0.12] = P[1.124864 - 1.12] = P(0.004864) = 30.4. Therefore P = 30.4/0.004864 = 6250. Verification: CI = 6250(1.04)³ - 6250 = 780.4; SI = 6250 × 0.04 × 3 = 750; difference = 30.4 ✓. Key distractor: 6000 (uses simple approximation).

Multiple choice

On a sum simple interest of 2 years is Rs. 450 and compound interest for same period is Rs. 495. Find the sum. एक मूलधन पर दो वर्षों का साधारण ब्याज 450 रूपये है तथा समान समय का चक्रवृद्धि ब्याज 495 रू. है। मूलधन ज्ञात कीजिये।

  1. Rs./रू.180

  2. Rs./रू.1260

  3. Rs./रू.960

  4. Rs./रू.1125
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let principal be P and rate be R%. Simple Interest for 2 years = P×R×2/100 = 450, so PR = 22500. Compound Interest for 2 years = P[(1+R/100)² - 1] = 495. Expanding: P[2R/100 + R²/10000] = 495. Using PR = 22500: 2×22500/100 + PR²/10000 = 495, so 450 + PR²/10000 = 495, PR²/10000 = 45. Since PR = 22500: R = 45×10000/22500 = 20%. Then P = 22500/20 = 1125.

Multiple choice

The difference in simple interest and compound interest on a certain sum of money in 3 years at 15% p.a. is Rs.453.6. The sum is-

  1. Rs. 6000

  2. Rs. 6200

  3. Rs. 6300

  4. Rs. 6400

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

The difference between compound and simple interest for 3 years at 15% is P[(1.15)³ - 1 - 0.45]. Solving: P[1.520875 - 1 - 0.45] = P[0.070875] = 453.6. Therefore P = 453.6/0.070875 = 6400. For verification: SI = 6400 × 0.15 × 3 = 2880. CI = 6400 × 0.520875 = 3333.6. Difference = 453.6.

Multiple choice

A principle of Rs. 18000 is deposited in a bank for two years which gives 20% rate of interest per annum compounded annually. If the given interest compounded half yearly then interest would have been how many percent more than its present interest.

  1. 5.4%

  2. 11.23%

  3. 9.45%

  4. 12.03%

  5. 7.45%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Principal = Rs. 18000, Rate = 20% p.a., Time = 2 years. Annual compounding: Amount = 18000 × (1.2)² = 18000 × 1.44 = 25920. Interest = 25920 - 18000 = 7920. Half-yearly compounding: Rate per half-year = 10%, Periods = 4. Amount = 18000 × (1.1)⁴ = 18000 × 1.4641 = 26353.8. Interest = 26353.8 - 18000 = 8353.8. Difference = 8353.8 - 7920 = 433.8. Percentage more = (433.8/7920) × 100 ≈ 5.4%. Option A is correct.

Multiple choice

Paritosh borrowed Rs.8000 at 4% simple interest and Arunesh borrowed Rs.6000 at 6% simple interest. After how much time they will have equal debts? परितोष ने रू. 8000 को 4% वार्षिक साधारण ब्याज की दर से तथा अरूणेश ने रू. 6000 को 6% वार्षिक साधारण ब्याज की दर से उधार लिया। कितने समय बाद दोनों का ऋण बराबर हो जाएगा?

  1. 25 years/वर्ष

  2. 15 years/वर्ष

  3. 40 years/वर्ष

  4. 50 years/वर्ष
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let t years be when debts are equal. Paritosh's debt after t years: 8000 + 8000 × 0.04 × t = 8000 + 320t. Arunesh's debt after t years: 6000 + 6000 × 0.06 × t = 6000 + 360t. Equating: 8000 + 320t = 6000 + 360t. Solving: 2000 = 40t, giving t = 50 years. After 50 years, Paritosh owes 8000 + 320(50) = 8000 + 16000 = 24000, and Arunesh owes 6000 + 360(50) = 6000 + 18000 = 24000, making option D correct.

Multiple choice

The simple interest on a sum of money for 3 years is Rs.240 and the compound interest on the same sum at the same rate for 2 years is Rs.70 less than the given simple interest. The sum of money is - एक धनराशि पर 3 वर्ष में साधारण ब्याज 240 रू. है और उसी धनराशि पर उसी ब्याज दर से 2 वर्ष में चक्रवृद्धि ब्याज दिए गए साधारण ब्याज से 70 रू. कम है। धनराशि है -

  1. Rs./रू. 1000

  2. Rs./रू. 620

  3. Rs./रू. 625

  4. Rs./रू. 640
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

SI for 3 years = 240, so SI for 1 year = 80. CI for 2 years = 240 - 70 = 170. Let principal = P, rate = r%. SI for 2 years = 2Pr/100 = 160 (since SI for 3 years = 240). So Pr = 8000. CI for 2 years = P(1 + r/100)² - P = 170. Using approximation: CI ≈ SI for 2 years + interest on first year's interest. First year interest = 80, second year interest on 80 = 80r/100. CI = 160 + 80r/100 = 170, so 80r/100 = 10, r = 12.5%. Then Pr = 8000 means P × 12.5 = 8000, P = 640. The claimed answer D is correct.

Multiple choice

Compound interest on certain sum at 15% per annum for 3 year is Rs. 6250.5. Find the principal. किसी धनराशि पर 15% प्रति वर्ष की दर से 3 वर्षों का चक्रवृद्धि ब्याज 6252.56 है मूलधन ज्ञात कीजिये।

  1. Rs. 18000

  2. Rs. 15000

  3. Rs. 20000

  4. Rs. 12000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Compound Interest formula: CI = P(1 + r/100)³ - P = 6250.5. At 15% for 3 years: CI = P(1.15)³ - P = P(1.520875) = 0.520875P. If P = 12000: CI = 12000 × 0.520875 = 6250.5 ✓. Option A (18000) would give CI = 9375.75. Option B (15000) would give CI = 7813.13. Option C (20000) would give CI = 10417.5. Note: Question states CI as 6250.5 in one place and 6252.56 in another - assuming 6250.5 is correct based on calculation.

Multiple choice

A sum of Rs.8360 is borrowed at 20% pa compounded interest and paid back in two equal annual instalments. What is the amount of each instalment? 8360 रुपए की राशि 20% प्रति वर्ष चक्रवृद्धि ब्याज पर उधार ली जाती है और दो समान वार्षिक किश्तों में वापस भुगतान किया जाता है । प्रत्येक किस्त की राशि क्या है?

  1. Rs. 5572

  2. Rs. 5472

  3. Rs. 6652

  4. Rs. 4572
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let each installment = x. After 1 year: amount = 8360 × 1.2 = 10032. After paying x: remaining = 10032 - x. After 2nd year: (10032 - x) × 1.2 = x. Solving: 12038.4 - 1.2x = x, 2.2x = 12038.4, x = 5472. Use the compound interest formula recursively, equating final amount to the second installment.

Multiple choice

A certain sum of money, invested at compound interest becomes Rs.3000 in 3 years and Rs.6000 in 6 years. Find the amount after 9 years. एक निश्चित धनराशि, चक्रवृद्धि ब्याज पर 3 वर्षों में 3000 रु. हो जाती है और 6 वर्षों में 6000 रु. हो जाती है | 9 वर्ष बाद धनराशि ज्ञात कीजिये |

  1. Rs. /रु.7500

  2. Rs. /रु.9000

  3. Rs. /रु.10000

  4. Rs. /रु.12000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In compound interest, if amount doubles every 3 years (3000 to 6000), the pattern continues: after 9 years = 12000. This follows the rule that in compound interest, when amount doubles over equal intervals, each interval doubles the amount. The 3-6 year doubling means 6-9 years also doubles.

Multiple choice

A person took a loan of Rs.15000 for 3 years, at 5% per annum compound interest. He repaid Rs.5250 in each of the first 2 years. The amount he should pay at the end of 3rd year to clear all his debts is किसी व्यक्ति ने 5% वार्षिक दर से चक्रवृद्धि ब्याज पर 3 वर्ष के लिये 15000 रू. का ऋण लिया। उसने पहले दो वर्षों में प्रति वर्ष 5250 रू. वापस किये। ऋण से मुक्त होने के लिए उसे तीसरे वर्ष में कितनी राशि देनी होगी?

  1. Rs./रू.6063.75

  2. Rs./रू.6381.25

  3. Rs./रू.6588.75

  4. Rs./रू.6863.75
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Year 1: Loan grows to 15000 × 1.05 = 15750. After payment: 15750 - 5250 = 10500. Year 2: Grows to 10500 × 1.05 = 11025. After payment: 11025 - 5250 = 5775. Year 3: Grows to 5775 × 1.05 = 6063.75, which is the final payment needed.

Multiple choice

The simple interest for four years is one fourth of the principal. The sum that will amount to Rs.2250 in two years at the same rate is - चार वर्षों का साधारण ब्याज मूलधन का एक चौथाई है। उसी दर से किस राशि का मिश्रधन दो वर्ष में 2250 रू. हो जायेगा?

  1. Rs./रू.1990

  2. Rs./रू.2500

  3. Rs./रू. 2000

  4. Rs./रू.2625
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let principal be P and rate be R%. Given: 4-year simple interest = P/4, so 4PR/100 = P/4. Solving: R = 100/16 = 6.25%. For 2 years at same rate: Amount = P + (2 × 6.25/100)P = 1.125P. Setting 1.125P = 2250 gives P = 2000. Check: 2-year SI on Rs.2000 at 6.25% is Rs.250, so amount = Rs.2250.

Multiple choice

The difference between compound interest and simple interest on a certain sum at 30% rate of interest per annum in two years is Rs.1080. Find the sum. यदि एक निश्चित धनराशि पर 30% वार्षिक ब्याज की दर से दो वर्षों में चक्रवृद्धि ब्याज और साधारण ब्याज में अन्तर 1080 रू. है। धनराशि ज्ञात कीजिये।

  1. Rs. /रू.10800

  2. Rs. /रू.15000

  3. Rs. /रू.18000

  4. Rs. /रू.12000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For 2 years at R = 30%: CI = P(1.3)² - P = 0.69P, SI = 2PR/100 = 0.6P. Difference = CI - SI = 0.69P - 0.6P = 0.09P. Given 0.09P = 1080, so P = 12000. Standard 2-year formula: CI - SI = PR²/10000. Here: P × 900/10000 = 1080, giving P = 12000. This difference is the 'interest on interest' for year 2.