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. 2600 is lent in two parts in such a way that the simple interest on one part at 10% for 5 years is equal to that on the other part at 9% (simple interest) for 6 years. The sum that is lent for 5 years at the rate of 10% is

  1. Rs. 1250

  2. Rs. 1350

  3. Rs. 1450

  4. Rs. 1550
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the two parts be x and 2600-x. Simple interest is (P*R*T)/100. Setting (x*10*5)/100 = ((2600-x)*9*6)/100 leads to 50x = 54(2600-x). Solving this gives 50x = 140400 - 54x, so 104x = 140400, x = 1350.

Multiple choice

If the simple interest on a certain sum of money for 3 years is Rs. 225 and the compound interest on the same sum at the same rate for 2 years is Rs. 153, then the principal invested (in Rs.) is

  1. Rs. 3000

  2. Rs. 1875

  3. Rs. 1500

  4. Rs. 2250

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

SI for 3 years = 225, so SI for 1 year = 75. Rate R = (75/P)*100. CI for 2 years = P(1+R/100)^2 - P = 153. P(1 + 75/P)^2 - P = 153. P(1 + 150/P + 5625/P^2) - P = 153. 150 + 5625/P = 153. 5625/P = 3. P = 1875.

Multiple choice

Raghav has to repay a loan of Rs. 12,820 in three annual instalments. The first instalment is to be half of the second and one-third of the third. If the compound interest is calculated annually at a rate of 10%, then find the value of the third instalment that Raghav has to pay.

  1. Rs. 5324

  2. Rs. 6934

  3. Rs. 7986

  4. Rs. 8986
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the installments be x, 2x, and 3x. The present value of these installments at 10% interest is x/(1.1) + 2x/(1.1)^2 + 3x/(1.1)^3 = 12820. Solving for x: x(0.909 + 1.653 + 2.254) = 12820. 4.816x = 12820. x is approx 2662. The third installment is 3x = 7986.

Multiple choice

A sum of money is accumulating at compound interest at a certain rate. If simple interest instead of compound was reckoned, the interest for the first two years would be diminished by Rs. 20 and that for the first three years by Rs. 61. Find the sum.

  1. Rs. 6500

  2. Rs. 7000

  3. Rs. 7500

  4. Rs. 8000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P be the sum and r be the rate. CI for 2 years = P(1+r)^2 - P = 2Pr + Pr^2. SI for 2 years = 2Pr. Difference = Pr^2 = 20. CI for 3 years = P(1+r)^3 - P = 3Pr + 3Pr^2 + Pr^3. SI for 3 years = 3Pr. Difference = 3Pr^2 + Pr^3 = 61. Divide: (3Pr^2 + Pr^3) / Pr^2 = 61/20. 3 + r = 3.05, so r = 0.05. Pr^2 = 20 => P(0.05)^2 = 20 => P(0.0025) = 20 => P = 8000.

Multiple choice

A lent B Rs. 900 for a certain time at a certain rate per annum which was equal to the square root of the number of months of time. After the time, B wanted to return the money, but A instead of taking the interest, which amounted to Rs. 48, asked for a certain sum of money at the same rate for a certain number of years which was equal to the square root of the rate. Find the sum of money so that neither of them ends up as a loser. (Take simple interest)

  1. Rs. 720

  2. Rs. 640

  3. Rs. 600

  4. Rs. 580
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let time be T months, rate be R% per annum. R = sqrt(T). Interest = (P * R * T_years) / 100. 48 = (900 * R * (T/12)) / 100. Substituting T = R^2, 48 = 9 * R * (R^2/12) = 0.75 * R^3. R^3 = 64, so R = 4. T = 16 months. The second part involves finding a sum P2 such that interest is equal. This leads to P2 = 600.

Multiple choice

A man earns 6% simple interest on his deposits in bank A while he earns 8% simple interest on his deposits in bank B. If the total interest he earns is Rs.1800 in three years on an investment of Rs.9000, what is the amount invested at 6%?

  1. 8000

  2. 6000

  3. 4000

  4. 3000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the amount at 6%. Then (9000-x) is at 8%. Interest = (x * 0.06 * 3) + ((9000-x) * 0.08 * 3) = 1800. 0.18x + 2160 - 0.24x = 1800. 0.06x = 360. x = 6000.

Multiple choice

The simple interest on a certain sum of money for 4 years at 4% per annum exceeds the compound interest on the same sum for 3 years at 5% per annum by Rs. 228. Find the sum.

  1. Rs. 96,000

  2. Rs. 91,000

  3. Rs. 86,000

  4. Rs. 81,000

  5. Rs. 80,000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the sum be P. Simple interest = P * 0.04 * 4 = 0.16P. Compound interest = P * (1 + 0.05)^3 - P = P * (1.157625 - 1) = 0.157625P. The difference is 0.16P - 0.157625P = 0.002375P = 228. Solving for P gives P = 228 / 0.002375 = 96,000.