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 man borrowed some money from a private organisation at 5% simple interest per annum. He lended 50% of this money to another person at 10% compound interest per annum and thereby the man made a profit of Rs. 3205 in 4 years. The man borrowed

  1. Rs. 80,000

  2. Rs. 1,00,000

  3. Rs. 1,20,000

  4. Rs. 1,50,000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the borrowed amount be P. At 5% simple interest for 4 years, interest payable = P × 5 × 4 / 100 = 0.2P. The man lends 50% of P (i.e., 0.5P) at 10% compound interest for 4 years. Using CI formula: Amount = 0.5P(1 + 10/100)^4 = 0.5P(1.1)^4 = 0.5P × 1.4641 = 0.73205P. Compound interest earned = 0.73205P - 0.5P = 0.23205P. Profit = CI earned - SI payable = 0.23205P - 0.2P = 0.03205P = Rs. 3205. Therefore, P = 3205 / 0.03205 = Rs. 1,00,000.

Multiple choice

Which of the following is the best investment option for the purpose of getting the maximum benefits of compounding?

  1. 12% interest paid yearly

  2. 6% interest paid every 6 months

  3. 3% interest paid every quarter

  4. 1% interest paid monthly
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

More frequent compounding yields higher returns. The effective annual rate for 1% monthly is (1.01)^12 - 1 = 12.68%, beating 12% yearly, 12.36% semi-annually, and 12.55% quarterly. Option D maximizes compounding benefits.

Multiple choice

With a 9% compound interest rate, your money will double in

  1. 5 Years

  2. 6 Years

  3. 7 Years

  4. 8 Years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the Rule of 72 for compound interest calculations, divide 72 by the interest rate to get the doubling time: 72/9 = 8 years. This is a close approximation for how long it takes an investment to double at a given compound interest rate. The exact calculation would be ln(2)/ln(1.09) which equals approximately 8.04 years.

Multiple choice

A Sum of Rs. 14280 is to be divided between Anshika and Aman who are respectively 18 and 19 years old, in such a way that if their shares will be invested at 4% per annum at compound interest, they will receive equal amounts on attaining the age of 21 years. The present share of Anshika is -

  1. 8450

  2. 8712

  3. 7000

  4. 8000

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

Let Anshika's share be x and Aman's share be (14280 - x). Anshika's money grows for 3 years (age 18 to 21) while Aman's grows for 2 years (age 19 to 21). At 4% compound interest: x(1.04)^3 = (14280 - x)(1.04)^2. Simplifying: 1.04x = 14280 - x, so 2.04x = 14280. Therefore x = 7000.

Multiple choice

Abhishek invested P for 2 years in scheme A which offered 20% p.a. compound interest (compounded annually). He lent the interest earned from scheme A to Maneesh, at the rate of 7.5% p.a. simple interest. If at the end of 2 years, Maneesh gave Rs. 3036 to Abhishek and thereby repaid the whole amount (actual loan + interest), what is the value of P?

  1. Rs. 6000

  2. Rs. 5800

  3. Rs. 6800

  4. Rs. 6400

  5. Rs. 5400
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Abhishek invests P at 20% compound interest for 2 years. Amount after 2 years = P(1.20)² = 1.44P. Interest earned = 1.44P - P = 0.44P. This interest is lent to Maneesh at 7.5% simple interest for 2 years. Simple interest = 0.44P × 7.5/100 × 2 = 0.066P. Total amount Maneesh repays = 0.44P + 0.066P = 0.506P. Given this equals Rs. 3036, so P = 3036/0.506 = Rs. 6000.

Multiple choice

A certain sum P when invested for four years at the rate of 10% p.a. simple interest, amounts to 22960. What will be the interest earned when (P + 600) is invested in the same rate of simple interest p.a. for four years?

  1. 6400

  2. 6800

  3. 6500

  4. 6600

  5. 6900
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For simple interest: Amount = Principal + Interest = P + (P × R × T)/100. Given 22960 = P + (P × 10 × 4)/100 = P + 0.4P = 1.4P. So P = 22960/1.4 = 16400. For (P + 600) = 17000 at 10% for 4 years, Interest = 17000 × 10 × 4/100 = 6800. The claimed answer 6800 is correct.

Multiple choice

Find the simple interest of 4 years and 5 months- Statement I: Ratio of SI and CI on principal for 2 years is 75:84. Statement II: Compound interest of 1 year and 6 months is 2430 Rs. Statement III: Compound interest of 2 years is 53.76% of the principal itself.

  1. Any two are sufficient

  2. II and (I or III) together are sufficient

  3. Only II and III together are sufficient

  4. All three together are sufficient

  5. Other than given options
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement III: CI of 2 years = 53.76% of principal. Using CI formula: P(1+r)² - P = 0.5376P, giving (1+r)² = 1.5376, so 1+r = 1.24, r = 24%. Statement II: CI for 1.5 years at 24% = P[(1.24)^1.5 - 1] = 2430, giving P = Rs 10000. Statement I: SI:CI ratio for 2 years is 75:84. At 24%, SI(2y) = 48%, CI(2y) = 53.76%. Ratio 48:53.76 simplifies to 75:84 (true). So I is redundant. II and III are sufficient. II gives P, III gives r. SI for 4y 5m = 10000 × 0.24 × (53/12) = Rs 10600. Option B is correct.

Multiple choice

Quantity I: The difference between the rate of CI and rate of depreciation if a person Akash has a sum of INR 5000 which after 3 years at compound interest @20% p.a. becomes a certain amount that is equal to the amount that is the result of 3-year compounded depreciation from INR 16875. \ Quantity II: 20%.

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relationship cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: CI rate is 20%. Depreciation: 16875 depreciates to 5000 in 3 years. 5000 = 16875(1-r)³, so (1-r)³ = 0.2963, 1-r ≈ 0.667, r ≈ 33.33%. Difference = 33.33% - 20% = 13.33%. Quantity II = 20%. Since 20% > 13.33%, Quantity II > Quantity I. Answer A is correct.

Multiple choice

A and B together borrowed a sum of Rs. 51750 at an interest rate of 7% p.a. compound interest in such a way that to settle the loan, A paid as much amount after three years as paid by B after 4 years from the day of borrowing. The sum (in Rs.) borrowed by A was:

  1. 24860

  2. 26750

  3. 25650

  4. 25000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A borrow amount 'a' and B borrow amount 'b'. At 7% compound interest, A pays a(1.07)³ after 3 years and B pays b(1.07)⁴ after 4 years. These amounts are equal: a(1.07)³ = b(1.07)⁴, so a = 1.07b. Given a + b = 51750, we get 2.07b = 51750, so b = 25000 and a = 26750. Options A and C are incorrect calculations.

Multiple choice

If the principal is Rs. 8000 and the rate is 20% per annum, what will be the difference between simple interest and compound interest in 1 year if the interest is compounded quarterly?

  1. 121.63

  2. 126.35

  3. 124.05

  4. 132.64
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple interest for 1 year at 20% on Rs 8000 = 8000×0.2×1 = Rs 1600. Compound interest compounded quarterly: rate per quarter = 20/4 = 5%, number of quarters = 4. CI = 8000×(1.05^4 - 1) ≈ 8000×(1.2155 - 1) ≈ Rs 1724.05. Difference = 1724.05 - 1600 = Rs 124.05.

Multiple choice

The rate of simple interest is 6% for the first 3 years, 7% for the next 4 years and 7.5% from 7 years onwards. A person invested Rs.56400 for 11 years. Find the simple interest?

  1. 35890

  2. 44360

  3. 36840

  4. 42864
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Calculate interest for each period separately. First 3 years at 6%: 56400×0.06×3 = Rs 10152. Next 4 years at 7%: 56400×0.07×4 = Rs 15792. Final 4 years at 7.5%: 56400×0.075×4 = Rs 16920. Total SI = 10152 + 15792 + 16920 = Rs 42864.

Multiple choice

Rs 2304 is kept at compound interest for 2 years. This amount becomes 2500 at 2 years at any rate. Find the rate of interest?
  1. $24/5$
  2. $23/3$
  3. $22/4$
  4. $25/6$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For compound interest: A = P(1 + r)ⁿ. Given P = 2304, A = 2500, n = 2. So 2500 = 2304(1 + r)². Then (1 + r)² = 2500/2304 = 625/576. Therefore 1 + r = 25/24, so r = 1/24 = 25/600 = 25/6%. Option A (24/5 = 4.8%) is incorrect. Option B (23/3 ≈ 7.67%) doesn't match. Option C (22/4 = 5.5%) is wrong. The answer 25/6% ≈ 4.17% is correct.