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

What sum of money at compound interest will amount to Rs. 4781.70 in three years if the rate of interest is 5% for the first year, 10% for the second year and 15% for the third year? किसी निश्चित राशि पर तीन वर्षो के बाद चक्रवृद्धि ब्याज की दर से 4781.70 रु. प्राप्त होते है। यदि प्रथम वर्ष ब्याज दर 5%,दूसरे वर्ष 10% और तीसरे वर्ष 15% हो तो राशि क्या थी ?

  1. 3280

  2. 3450

  3. 3600

  4. 3720

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

Work backwards from final amount. After 3rd year at 15%: Amount/1.15. After 2nd year at 10%: Amount/(1.15×1.1). After 1st year at 5%: Amount/(1.15×1.1×1.05) = 4781.70/1.33575 = 3600. This is the principal amount.

Multiple choice

The simple interest on a sum of money at 10% per annum for 2 years is Rs. 8,100. Compounded annually, what would be the compound interest (in Rs.) on the same sum for the same period at the same rate of interest?

  1. 8100

  2. 8505

  3. 8715

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

SI = P*10*2/100 = 8100, so P = 40500. CI = P(1 + 10/100)^2 - P = 40500(1.21 - 1) = 40500*0.21 = 8505. The compound interest is Rs. 8505, which is Rs. 405 more than the simple interest due to interest on interest.

Multiple choice

₹ 4,300 becomes ₹ 4,644 in 2 years at simple interest. Find the principle amount that will become ₹ 10,104 in 5 years at the same rate of interest.

  1. ₹ 7,200

  2. ₹ 8,420

  3. ₹ 9,260

  4. ₹ 5,710
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For the first investment: Principal = ₹4,300, Amount = ₹4,644, Time = 2 years. Simple Interest = 4,644 - 4,300 = ₹344. Rate r = (SI × 100) ÷ (P × T) = (344 × 100) ÷ (4,300 × 2) = 34,400 ÷ 8,600 = 4% per annum. For the second case: Let new principal be P, Amount = ₹10,104, Time = 5 years, Rate = 4%. SI = Amount - P = 10,104 - P. Using SI = (P × R × T) ÷ 100: 10,104 - P = (P × 4 × 5) ÷ 100 = 20P ÷ 100 = 0.2P. So 10,104 = P + 0.2P = 1.2P. Therefore P = 10,104 ÷ 1.2 = ₹8,420.

Multiple choice

The compound interest on a certain sum for 2 years at 15% per annum is Rs. 3,641, when the interest is compounded 8-monthly. The sum is:

  1. 9000

  2. 9600

  3. 11000

  4. 10000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For 8-monthly compounding at 15% p.a., the rate per 8-month period is 15% × (8/12) = 10%. In 2 years, there are 2 × 12/8 = 3 periods. Using CI = P[(1 + r)^n - 1], we get 3641 = P[(1.10)³ - 1] = P[1.331 - 1] = P(0.331). Therefore, P = 3641/0.331 = Rs. 11,000.

Multiple choice

The simple interest on a sum of Rs. 4,800 for 4.5 years at a certain rate per annum is Rs. 1,684.80, What will be the amount of the same sum at the same rate for 6.67 years at simple interest?

  1. 7096

  2. 7087

  3. 7296

  4. 7298
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First find the rate: SI = P×R×T gives 1684.80 = 4800×R×4.5, so R = 1684.80/(4800×4.5) = 7.816% p.a. For 6.67 years at the same rate: SI = 4800×0.07816×6.67 = Rs. 2496. Amount = Principal + SI = 4800 + 2496 = Rs. 7296.

Multiple choice

On a principal difference of SI and CI of two year is Rs. 120 whereas difference of SI and CI of three years is Rs 368. Find the rate of interest. किसी मूलधन पर दो वर्ष का साधारण ब्याज तथा चक्रवृधि ब्याज का अन्तर 48 रुपये हैं जबकि तीन वर्ष के साधारण ब्याज तथा चक्रवृधि ब्याज का अन्तर 368 रुपये है। ब्याज दर ज्ञात कीजिये।

  1. 6.25%

  2. 7.25%

  3. 7.5%

  4. 6.67%

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

The English text states the 2-year difference is Rs. 120, but the Hindi text says it's Rs. 48. The 3-year difference is consistently Rs. 368. Using the Hindi figure (48): D2 = P(r/100)² = 48, D3 = P(r/100)²(3 + r/100) = 368. Dividing: (3 + r/100) = 368/48 = 23/3, so r/100 = 23/3 - 3 = 14/3, r = 1400/3 ≈ 46.67%. This is not in options. Using English figure (120): P(r/100)² = 120, and (3 + r/100) = 368/120 = 23/7.5, so r/100 = 23/7.5 - 3 ≈ 0.067, r ≈ 6.67%. This matches option D. The Hindi figure appears to be an error.

Multiple choice

Seven copies of a book can be bought for the certain sum payable at the end of a year and eight copies of the same book can be bought for the same sum in ready money; what is the rate percentage (correct up to two decimal places) of interest?

  1. 11.56

  2. 14.29

  3. 12.25

  4. 15.04
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is equivalent to: 7 copies at year-end price (with interest) = 8 copies at ready money price. Let rate = r%. Then 7(1 + r/100) = 8, giving 1 + r/100 = 8/7, so r = 100/7 = 14.29%. This relationship comes from the fact that with simple interest, the future value equals present value times (1 + rate). Option B is correct.

Multiple choice

The difference between the interest received by Anil and Ravi is Rs 120. When they invest Rs 2000 each for 3 years what is the difference in the rate of interest?

  1. 2%

  2. 7%

  3. 4%

  4. 6%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the rates be r1 and r2 for Anil and Ravi respectively. Interest for 3 years at simple interest: I = P × r × t / 100. Difference in interest = 2000 × r1 × 3 / 100 - 2000 × r2 × 3 / 100 = 120. Simplifying: 2000 × 3 × (r1 - r2) / 100 = 120. So 60 × (r1 - r2) = 120, giving (r1 - r2) = 2%. The difference in rates is 2%.

Multiple choice

A certain sum is deposited for 4 years at a rate of 10% per annum on compound interest compounded annually. The difference between the interest at the end of 2 years and that at the end of 4 years is ₹5,082. Find the sum (in ₹).

  1. 20,000

  2. 25,500

  3. 50,820

  4. 10,164
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For principal P, after 2 years: A2 = P(1.1)² = 1.21P. After 4 years: A4 = P(1.1)⁴ = 1.4641P. Difference in interest = A4 - A2 = 1.4641P - 1.21P = 0.2541P = 5,082. Therefore P = 5,082/0.2541 = Rs 20,000.

Multiple choice

A man invested Rs X in a scheme A at the rate of 10% compounded annually for 2 years. Man invested total amount received from scheme A in another Scheme B at the rate of 5% for 2 years at simple interest. find the interest received from scheme B is what % of interest received from Scheme A?
  1. $62.56%$
  2. $54.89%$
  3. $57.61%$
  4. $44.67%$
  5. $58.23%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

After 2 years at 10% compound interest, amount = X(1.1)² = 1.21X. Interest from scheme A = 0.21X. This 1.21X invested at 5% simple interest for 2 years gives interest = 1.21X × 0.05 × 2 = 0.121X. Required percentage = (0.121X / 0.21X) × 100 = 57.61%.

Multiple choice

A sum of money at compound interest double itself in 13 years. It will become eight times of itself in एक राशि चक्रवृद्धि ब्याज पर 13 वर्ष में अपने आप की दुगनी हो जाती है। यह अपने की आठ गुनी हो जाएगी:

  1. 45 years 45 साल

  2. 48 years 48 साल

  3. 54 years 54 साल

  4. 60 years 60 साल

  5. 39 years 39 साल
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

If amount doubles in 13 years, then 2P = P(1 + r)^13, so (1 + r)^13 = 2. To become 8 times: 8P = P(1 + r)^n, so (1 + r)^n = 8 = 2^3. Since (1 + r)^13 = 2, we need (1 + r)^(13×3) = 2^3, so n = 13 × 3 = 39 years.

Multiple choice

Ram lends Rs. 20,000 to two of his friends. He gives Rs. 12,000 to the first at 8% p.a. simple interest. Ram wants to make a profit of 10% on the whole. The simple interest rate at which he should lend the remaining sum of money to the second friend is राम अपने दो दोस्तों को 20000 का उधार देता है वह पहले दोस्त को 12000 , 8 % साधारण व्याज के दर पर देता है और पूरे पर 10 % का लाभ कमाना चाहता है तो दूसरे दोस्त को किस दर पर उधार देना चाहिए ?

  1. 16%

  2. 15%

  3. 12%

  4. 13%

  5. 8%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total amount = Rs. 20,000. First loan = Rs. 12,000 at 8% p.a. Interest from first loan = 12000 × 0.08 = Rs. 960. Desired profit on whole = 10% of 20000 = Rs. 2000. So second loan interest needed = 2000 - 960 = Rs. 1040. Second loan amount = 20000 - 12000 = Rs. 8000. Rate = 1040/8000 = 0.13 = 13%.