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

An usurer claims to be lending money at simple interest. But, he includes the interest every six months for calculating the principal. If he is charging an interest of 15%, then the effective rate of interest becomes

  1. 15.56%

  2. 15%

  3. 16%

  4. 15.65%

  5. 15.75%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The interest is compounded semi-annually. The effective rate is calculated as (1 + r/n)^n - 1, where r = 0.15 and n = 2. This gives (1 + 0.15/2)^2 - 1 = (1.075)^2 - 1 = 1.155625 - 1 = 0.155625, or 15.56%.

Multiple choice

The compound interest accrued on an amount of Rs. 16800 at the end of two years was Rs. 5418. What would be the simple interest accrued on the same amount at the same rate for the same period?

  1. Rs. 5070

  2. Rs. 5040

  3. Rs. 5210

  4. Rs. 5280

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

CI = P[(1+r/100)^2 - 1] = 5418. 16800[(1+r/100)^2 - 1] = 5418. (1+r/100)^2 - 1 = 0.3225. (1+r/100)^2 = 1.3225. 1+r/100 = 1.15. r = 15%. SI = P*r*t/100 = 16800 * 0.15 * 2 = 5040.

Multiple choice

How can Rs. 3903 be divided between A and B today so that A's share at the end of 7 years is equal to B's share at the end of 9 years at 4% p.a. rate of compound interest?

  1. Rs. 2233, Rs. 1670

  2. Rs. 2125, Rs. 1778

  3. Rs. 2075, Rs. 1828

  4. Rs. 2028, Rs. 1875

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

A * (1 + 0.04)^7 = B * (1 + 0.04)^9. This simplifies to A = B * (1.04)^2 = B * 1.0816. A + B = 3903. Substituting A: B * 1.0816 + B = 3903 => 2.0816 * B = 3903 => B = 1875. A = 3903 - 1875 = 2028.

Multiple choice

A sum of money is invested at simple interest and the same amount is invested at the same rate of compound interest for one year compounded annually. What will be the minimum time in which the amount invested at simple interest becomes equal to the amount with the compound interest?

  1. 1 year

  2. 2 years

  3. 3 years

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

For 1 year, simple interest and compound interest (compounded annually) are identical. Thus, the minimum time is 1 year.

Multiple choice

A person lent out a certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25 : 8. The rate of interest per annum is

  1. 10%

  2. 11%

  3. 12%

  4. 12 .5%

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

Difference for 2 years = P(r/100)^2. Difference for 3 years = P(r/100)^2 * (3 + r/100). Ratio = (3 + r/100) = 25/8. r/100 = 25/8 - 3 = 1/8. r = 12.5%.

Multiple choice

There are three investment schemes P, Q and R available in Bank Y. Schemes P and Q respectively offer 14% and 18% interest rates compounded annually, while scheme R offers 16% simple interest. Rakesh invests Rs. 16,000 in scheme R and Rs. 18,000 in scheme Q for two years, while Dharmesh invests Rs. 15,000 in scheme Q and Rs. 29,000 in scheme P for two years. What percent more interest will Dharmesh receive in comparison to Rakesh?

  1. 14.35%

  2. 16.58%

  3. 19.63%

  4. 20.35%

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

First, calculate Rakesh's total interest: Rs. 5,120 from scheme R and Rs. 7,063.20 from scheme Q, totaling Rs. 12,183.20. Next, calculate Dharmesh's total interest: Rs. 5,886 from scheme Q and Rs. 8,688.40 from scheme P, totaling Rs. 14,574.40. The percentage by which Dharmesh's interest exceeds Rakesh's is (14,574.40 - 12,183.20) / 12,183.20 * 100, which is approximately 19.63%.