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. $18750$ is left by will by a father to be divided between two sons, $12$ and $14$ years of age, so that when they attain maturity at $18$, the amount received by each of them at $5$ per cent simple interest will be the same. Find the sum allotted at present to each son?
  1. Rs. $9500$, Rs. $9250$
  2. Rs. $8000$, Rs. $1750$
  3. Rs. $9000$, Rs. $9750$
  4. Rs. $10000$, Rs. $8750$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let sums be x and y. x+y = 18750. Time for first son = 18-12 = 6 years. Time for second son = 18-14 = 4 years. Amount = P(1 + rt/100). x(1 + 0.05*6) = y(1 + 0.05*4). 1.3x = 1.2y. y = 1.3/1.2 x = 13/12 x. x + 13/12 x = 18750. 25/12 x = 18750. x = 18750 * 12 / 25 = 9000. y = 18750 - 9000 = 9750.

Multiple choice

Rs. $1000$ invested at $5\%$ p.a simple interest, if the interest is added to the principle after every $10$ years, the amount will become Rs. $2000$ after
  1. $15$ years
  2. $\displaystyle 16\frac{2}{3}$ years
  3. $18$ years
  4. $20$ years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial 1000. After 10 years, interest = 1000 * 0.05 * 10 = 500. New principal = 1500. We need 500 more interest. 500 = 1500 * 0.05 * t. t = 500 / 75 = 6.66 years. Total time = 10 + 6.66 = 16.66 years.

Multiple choice

Two equal sums of money are lent at the same time at $8\%$ and $7\%$ per annum simple interest. The former is recovered $6$ months earlier than the later and the amount in each case is Rs. $2560$. The sum and time for which the sums of money are lent out are
  1. Rs. $1500, 3.5$ year and $4$ year
  2. Rs. $2000, 3.5$ years and $4$ years
  3. Rs. $2000, 4$ years and $5.5$ years
  4. Rs. $3000, 4$ years and $4.5$ years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the sum be P and time be T. Amount = P + P*R*T/100. 2560 = P(1 + 0.08T) and 2560 = P(1 + 0.07(T+0.5)). Solving these equations: P(1 + 0.08T) = P(1 + 0.07T + 0.035) => 0.01T = 0.035 => T = 3.5 years. P = 2560 / (1 + 0.08*3.5) = 2560 / 1.28 = 2000.

Multiple choice

Anand deposited Rs. $6000$ on simple interest. He withdraw Rs. $4000$ and its interest from that amount after $2$ years. After next $3$ years, he withdraw the rest of the amount and its interest accured till that time, in all the obtained Rs. $900$ as interest. The rate of interest per annum was
  1. $3\%$
  2. $4\%$
  3. $5\%$
  4. $6\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let R be the rate. Interest for the first 2 years on 6000 is (6000*R*2)/100 = 120R. After withdrawing 4000, 2000 remains for 3 years, earning (2000*R*3)/100 = 60R. Total interest 120R + 60R = 180R = 900, so R = 5%.

Multiple choice

Divide Rs 2000 into two sums such that, if the first be put out at simple interest for 6 years at $\displaystyle 3\frac{1}{2}$ per cent and the second for 3 years at $\displaystyle 4\frac{1}{2}$ per cent, the interest on the first sum shall be double that of the second.

  1. Rs 725 Rs 1275

  2. Rs 1125, Rs 875

  3. Rs 1500, Rs 500

  4. Rs 635, Rs 1365
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the parts be x and 2000-x. Interest 1 = x * 3.5 * 6 / 100 = 0.21x. Interest 2 = (2000-x) * 4.5 * 3 / 100 = 0.135(2000-x). Setting 0.21x = 2 * 0.135(2000-x) gives 0.21x = 0.27(2000-x), so 0.48x = 540, x = 1125.

Multiple choice

A man deposited Rs. $6000$ in a bank at $5\%$ simple interest. Another man deposited Rs. $5000$ at $8\%$ compound interest. After $2$ years, the difference of their interest will be
  1. Rs. $230$
  2. Rs. $232$
  3. Rs. $600$
  4. Rs. $832$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simple interest for the first man is (6000 * 5 * 2) / 100 = Rs. 600. Compound interest for the second man is 5000 * ((1 + 8/100)^2 - 1) = 5000 * (1.1664 - 1) = Rs. 832. The difference is 832 - 600 = Rs. 232.