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. 1300 is lent in two parts so that interest on the first part for 3 year at 5% may be equal to the interest on the second part for 4 year at 6%. Find the first sum lent. 1300 रुपये की राशि को दो हिस्सों में ऐसे दिया गया है कि पहले हिस्से पर 5% ब्याज पर 3 वर्ष के लिए दूसरे हिस्से पर 6% ब्याज पर 4 वर्ष के लिए ब्याज के बराबर हो । पहला हिस्सा ज्ञात कीजिये।

  1. Rs. 1000

  2. Rs. 900

  3. Rs. 800

  4. Rs. 700
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let first part = x, then second part = 1300 - x. Interest on first part: (x × 5 × 3)/100 = 15x/100. Interest on second part: ((1300-x) × 6 × 4)/100 = 24(1300-x)/100. Setting equal: 15x = 24(1300 - x), so 15x = 31200 - 24x, therefore 39x = 31200 and x = 800. First sum = Rs. 800. Options A, B, D don't satisfy the condition of equal interest.

Multiple choice

What is the different between the compound interest and simple interest on a sum of Rs.64000 at 6% per annum for 3 years? 64000 रु. की एक धनराशि पर 6% वार्षिक ब्याज की दर से 3 वर्षों का चक्रवृद्धि ब्याज और साधारण ब्याज का अन्तर क्या है?

  1. Rs./रु.705.240

  2. Rs./रु.750.240

  3. Rs./रु.705.024

  4. Rs./रु.750.024
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For Rs. 64000 at 6% for 3 years: Simple Interest = (64000 × 6 × 3)/100 = Rs. 11520. Compound Interest = 64000(1 + 6/100)³ - 64000 = 64000[(1.06)³ - 1] = 64000(1.191016 - 1) = Rs. 12225.024. Difference = 12225.024 - 11520 = Rs. 705.024.

Multiple choice

The simple interest on a certain sum for 8 months at 4% per annum is 129 less than the simple interest on the same sum for 15 months at 5% per annum. The sum is- एक धनराशि पर 4% वार्षिक ब्याज की दर से 8 माह का साधारण ब्याज उसी धनराशि पर 15 माह के लिए 5% वार्षिक ब्याज की दर से साधारण ब्याज से 129 कम है । धनराशि है-

  1. 2580

  2. 2400

  3. 2529

  4. 3600
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let sum = P. SI at 4% for 8 months = P × 4 × 8/100 × 12 = 8P/2400. SI at 5% for 15 months = P × 5 × 15/100 × 12 = 75P/2400. Difference: 75P/2400 - 8P/2400 = 67P/2400 = 129. Solving: P = 129 × 2400/67 = 3600. Therefore, the sum is Rs. 3600.

Multiple choice

A sum of money amounts to Rs.12322.8 after 7 years and Rs.15724.8 after 12 years at the same rate of simple interest. What is the rate of interest per annum?

  1. 5%

  2. 7%

  3. 8%

  4. 10%

  5. 9%
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

After 7 years: P + SI(7) = 12322.8. After 12 years: P + SI(12) = 15724.8. Difference for 5 years = 15724.8 - 12322.8 = 3402. So SI for 5 years = 3402, meaning SI for 1 year = 3402/5 = 680.4. SI for 7 years = 680.4 x 7 = 4762.8. Principal = 12322.8 - 4762.8 = 7560. Rate = (680.4/7560) x 100 = 9%. Option E is correct.

Multiple choice

Find the principal which was invested- Statement I: Compound interest of 4 years was 107.36% of principal. Statement II: Simple interest of 2 years was Rs. 440. Statement III: Compound interest of 2 years was Rs. 484.

  1. I and III

  2. II and I or III

  3. Any two

  4. All three together are sufficient

  5. All three together are not sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: CI for 4 years is 107.36% of P. Using CI formula, we can find the rate. Statement II: SI for 2 years is Rs. 440, so P×R×2/100 = 440. Statement III: CI for 2 years is Rs. 484, giving another equation. With any two statements, we have two equations to solve for P and R. The claimed answer 'Any two' is correct because different pairs can solve for the principal.

Multiple choice

X borrowed Rs. 10,000 from his friend at 15% per annum simple interest. He lent it to Y at the same rate but compounded annually. Find his gain after two years.

  1. 200 Rs.

  2. 185 Rs.

  3. 225 Rs.

  4. 245 Rs.

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

At simple interest, X pays Rs. 13,000 after 2 years (Rs. 10,000 + Rs. 3,000 interest). At compound interest, Y pays Rs. 13,225 (Rs. 10,000 × 1.15²). The difference of Rs. 225 is X's gain from the interest rate differential.

Multiple choice

The difference between the compound interest and the simple interest on a certain sum at 18% per annum for 3 years is Rs. 489.402 the sum is - किसी धनराशि पर 18% वार्षिक दर पर 3 वर्षों के चक्रवृद्धि ब्याज और साधारण ब्याज का अंतर 489.402 रूपये है तो वह धनराशि कितनी है?

  1. Rs.4750

  2. Rs.4950

  3. Rs.4350

  4. Rs.5350
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

CI - SI for 3 years at 18% = P[(1 + 18/100)³ - 1] - P × 18 × 3/100 = P[1.18³ - 1 - 0.54] = P[0.643 - 0.54] = 0.103P = 489.402. Therefore P = 4750.

Multiple choice

At the same rate of simple interest sum of the interest of Rs. 3000 for 4 years and 8 months and the interest for 3 years and 9 months is 4292.5. The rate of interest is - एक समान साधारण ब्याज की दर पर 3000 रूपये का 4 वर्षों और 8 माह के ब्याज और 3 वर्षों और 9 माह के ब्याज का योगफल 4292.5 रूपये है तो ब्याज की दर कितनी है?

  1. 14%

  2. 15%

  3. 16%

  4. 17%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using simple interest formula and solving the equation 3000 × r × (4 + 8/12 + 3 + 9/12)/100 = 4292.5 gives r = 17%. This is a standard simple interest rate problem.

Multiple choice

Rs. 675 amounts to Rs. 837 in four years at simple interest. If the interest rate is decreased by 2%, then amount will be- 675 रू. की धनराशि साधारण ब्याज पर 4 वर्ष में 837 रू. हो जाती है। यदि ब्याज की दर में 2% कमी हो जाय तो धनराशि होगी-

  1. Rs.729

  2. Rs.753

  3. Rs.763

  4. Rs.783
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

SI = 837 - 675 = 162 for 4 years. Annual SI = 162/4 = 40.5. Rate = (40.5/675) × 100 = 6%. New rate = 4%. New SI for 4 years = 675 × 4 × 4/100 = 108. New amount = 675 + 108 = 783.

Multiple choice

If the ratio between the difference between compound interest and simple interest of 3 years and 2 years on a same sum is 16 : 5, then find the rate of interest.

  1. 20%

  2. 25%

  3. 10%

  4. 15%

  5. 12.5%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a sum P at rate r%, CI-SI difference for 2 years = Pr²/100² and for 3 years = Pr²(300+r)/100³. Ratio = [Pr²(300+r)/100³] / [Pr²/100²] = (300+r)/100 = 16/5. Solving: 5(300+r) = 1600, so 1500 + 5r = 1600, giving r = 20%. The pattern holds: check SI for 2 years = 2Pr/100, CI = P(1+r/100)² - P = Pr²/100² + 2Pr/100.

Multiple choice

P invested certain amount in two different schemes A and B . Scheme A offer simple interest at the rate of 12% per annum and scheme B offer compound interest at the rate of 10% percent per annum. Interest accured on the amount invested in scheme A in 2 years was Rs. 4800 and the total amount invested was Rs 51823 what was the interest accured on the amount invested in scheme B for 2 years?

  1. 6682.83

  2. 5482.83

  3. 3622.83

  4. 986.83

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

For Scheme A (12% SI for 2 years = 4800): Principal = 4800÷(12×2) = 20000. Total investment = 51823, so Scheme B investment = 51823-20000 = 31823. For Scheme B (10% CI for 2 years): Amount = 31823×(1.1)² = 31823×1.21 = 38505.83. Interest = 38505.83-31823 = 6682.83. Option A is correct.

Multiple choice

Cost price of freeze is Rs.20000. A customer purchase this on a cash down payment of Rs.5000 and promise to pay remaining amount in three equal annual instalment. If the rate of compound interest is 12.5% per annum, then find the value of each instalment?

  1. Rs.1020

  2. Rs.3816

  3. Rs.6299

  4. Rs.6300

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

Balance after down payment: 20000-5000=15000. For compound interest at 12.5%, PV factor = 1/(1.125)^t. PV of 3 installments = I[1/1.125 + 1/(1.125)^2 + 1/(1.125)^3] = I[0.8889 + 0.7901 + 0.7023] = I × 2.3813. Setting equal to 15000: I = 15000/2.3813 = Rs. 6299. Option C is correct.