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

Priya wants to find the simple interest for a period of 2 years such that it has the same rate of interest as compound interest amounts to Rs. 204 compounded for two years at the rate of interest of 4%. What will be the simple interest for two years?

  1. Rs. 200

  2. Rs. 150

  3. Rs. 195

  4. Rs. 170

  5. Rs. 180
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Compound interest for 2 years at 4% on P: P(1.04)^2 - P = 204. P(1.0816 - 1) = 204. P(0.0816) = 204. P = 2500. Simple interest = P * R * T / 100 = 2500 * 4 * 2 / 100 = 200.

Multiple choice

A, B and C borrow Rs. 29,200 in all at 4% simple interest and pay back equal amounts in full settlement of their respective debts after 5, 10 and 15 years, respectively. Find the sum borrowed by C.

  1. Rs. 11,200

  2. Rs. 9,600

  3. Rs. 8,400

  4. Rs. 7,600
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A, B, C borrow x, y, z. x + y + z = 29200. Amounts are equal: x(1 + 0.04*5) = y(1 + 0.04*10) = z(1 + 0.04*15). 1.2x = 1.4y = 1.6z. x = 1.6z/1.2 = 4/3 z. y = 1.6z/1.4 = 8/7 z. (4/3 + 8/7 + 1)z = 29200. (28/21 + 24/21 + 21/21)z = 29200. 73/21 z = 29200. z = 29200 * 21 / 73 = 400 * 21 = 8400.

Multiple choice

Seth Ankoosh Gawdekar borrows a sum of Rs. 1200 at the beginning of a year. After 4 months, Rs.1800 more is borrowed at a rate of interest double the previous one. At the end of the year, the sum of interest on both the loans is Rs. 216. What is the first rate of interest per annum?

  1. 9%

  2. 6%

  3. 8%

  4. 12%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let rate be R. Interest 1 = (1200 * R * 1) / 100 = 12R. Interest 2 = (1800 * 2R * 8/12) / 100 = 24R. Total interest = 36R = 216. R = 6%.

Multiple choice

A sum of Rs. 9400 is divided into three parts, such that the simple interests accrued on these sums for three, four and five years are equal. Find the amount deposited for five years.

  1. Rs. 5000

  2. Rs. 4000

  3. Rs. 2400

  4. Rs. 3000

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

Let the parts be P1, P2, P3. Simple interest is P*R*T/100. Since interests are equal, P1*3 = P2*4 = P3*5 = K. P1=K/3, P2=K/4, P3=K/5. Sum = K(1/3 + 1/4 + 1/5) = K(47/60) = 9400. K = 12000. P3 (for 5 years) = 12000/5 = 2400.

Multiple choice

Shweta borrowed some money under simple interest. If she pays Rs. 10,000 at the end of 1 year and Rs. 18,200 at the end of second year, the debt will be cleared. Even if she pays Rs. 15,000 at the end of 1 year and Rs. 12,800 at the end of second year, then also the debt will be cleared. What is the rate of interest?

  1. 8%

  2. 9%

  3. 10%

  4. 11%

  5. 12%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let P be the principal and r be the rate of interest. The two scenarios provide equations: P(1+r) + P(1+2r) = 10000 + 18200 and P(1+r) + P(1+2r) = 15000 + 12800. Solving these systems leads to a rate of 8%.

Multiple choice

The difference between compound interest and simple interest on a certain sum of money after 2 years at 10% rate of interest is Rs. 200. Find the difference in the interests after 3 years.

  1. Rs. 620

  2. Rs. 600

  3. Rs. 400

  4. Rs. 420

  5. Rs. 300
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For 2 years, the difference between CI and SI is P(r/100)^2. Given 200 = P(0.1)^2, P = 20000. For 3 years, the difference is P(r/100)^2 * (3 + r/100) = 200 * (3 + 0.1) = 200 * 3.1 = 620.

Multiple choice

A man borrows a sum of money at simple interest at the rate of 5% per annum and lends it out at 4% per annum compound interest, payable yearly. Find his net gain or loss at the end of 2 years as a percentage of sum borrowed by him.

  1. 2.52% gain

  2. 2.36% loss

  3. 1.84% loss

  4. 1.48% gain

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

Let sum be 100. SI paid = 5% * 2 = 10. CI earned = 100 * (1.04^2 - 1) = 100 * (1.0816 - 1) = 8.16. Net loss = 10 - 8.16 = 1.84.

Multiple choice

Amit invested two equal sums of Rs. 5000 for 2 years at 10%, one at compound interest payable yearly and the other at compound interest payable half-yearly. Find the difference between amounts that he will get at the end of 2 years.

  1. Rs. 23.50

  2. Rs. 24.50

  3. Rs. 25.50

  4. Rs. 27.50
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For yearly compounding, A = 5000(1 + 0.10)^2 = 6050. For half-yearly compounding, A = 5000(1 + 0.05)^4 = 5000(1.21550625) = 6077.53. The difference is 6077.53 - 6050 = 27.53, which is closest to 27.50.

Multiple choice

A borrowed Rs. 20,000 from B, at 10% p.a. compound interest. After 1 year, again A borrowed Rs. 10,000 from B at the same rate. Exactly after 1 more year, A won a lottery and wanted to repay the debt. How much would he have to pay to B?

  1. Rs. 34,000

  2. Rs. 34,200

  3. Rs. 35,200

  4. Rs. 35,000

  5. Rs. 36,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First loan of 20,000 grows for 2 years: 20000 * (1.1)^2 = 24200. Second loan of 10,000 grows for 1 year: 10000 * 1.1 = 11000. Total = 24200 + 11000 = 35200.

Multiple choice

Sachin borrowed Rs. 28000 from Yuvraj at 12% simple interest. After 1 year, he paid the interest and Rs. 10000 extra. After 6 months more, if Sachin wants to clear the debt, then how much money does he have to pay Yuvraj?

  1. Rs. 19080

  2. Rs. 22440

  3. Rs. 26000

  4. Rs. 21840

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

Interest for 1 year on 28000 at 12% is 3360. Total paid after 1 year is 3360 + 10000 = 13360. Remaining principal is 28000 - 10000 = 18000. Interest on 18000 for 6 months (0.5 years) at 12% is 18000 * 0.12 * 0.5 = 1080. Total to clear debt is 18000 + 1080 = 19080.