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

Sita invests Rs. 5,000 in a scheme that offers 8% per annum simple interest and Rs. 5,000 in another scheme that offers 8% per annum compound interest, both for 3 years. What is the difference in the amount of interest earned from both schemes?

  1. Rs. 94.76

  2. Rs. 96.66

  3. Rs. 98.56

  4. Rs. 99.65

  5. Rs. 100.56
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple interest = 5000 * 0.08 * 3 = 1200. Compound interest = 5000 * ((1 + 0.08)^3 - 1) = 5000 * (1.259712 - 1) = 1298.56. The difference is 1298.56 - 1200 = 98.56.

Multiple choice

Lata takes a loan of Rs. 10,000 at an annual compound interest rate of 10%, compounded annually, and agrees to repay it in 3 equal yearly installments. What is the approximate amount of each installment?

  1. Rs. 3,550

  2. Rs. 3,675

  3. Rs. 4,021

  4. Rs. 4,120

  5. Rs. 4,240
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The installment formula for compound interest is P = X / (1+r) + X / (1+r)^2 + X / (1+r)^3. Solving 10000 = X(1/1.1 + 1/1.21 + 1/1.331) gives X = 10000 / 2.48685 = 4021.15.

Multiple choice

Ajay takes a loan of Rs. 19,860 to buy a bike, to be repaid in 3 equal annual installments. The bank charges an interest rate of 10% per annum on the outstanding balance. How much should Ajay pay each year?

  1. Rs. 7,150

  2. Rs. 7,190

  3. Rs. 7,986

  4. Rs. 7,290

  5. Rs. 7,340
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is an annuity problem. P = 19860, r = 0.1, n = 3. Formula: P = X * [1 - (1+r)^-n] / r. 19860 = X * [1 - (1.1)^-3] / 0.1. 19860 = X * [1 - 0.7513] / 0.1. 19860 = X * 2.4868. X = 19860 / 2.4868 = 7986.

Multiple choice

Sunita purchased a home appliance worth Rs. 52,000 on an instalment plan. She pays Rs. 10,000 upfront, and the rest in 2 equal annual instalments. The interest rate is 10% on the remaining balance. What is the amount of each instalment?

  1. Rs. 20,340

  2. Rs. 22,400

  3. Rs. 24,200

  4. Rs. 24,700

  5. Rs. 25,200
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Remaining balance = 52000 - 10000 = 42000. Let x be the installment. The balance after 1st year is 42000 * 1.1 - x. The balance after 2nd year is (42000 * 1.1 - x) * 1.1 - x = 0. 42000 * 1.21 - 1.1x - x = 0. 50820 = 2.1x. x = 50820 / 2.1 = 24200.

Multiple choice

A small business owner has a debt of ₹1,19,600 due in 4 years. The debt is to be repaid in annual installments, with a simple interest rate of 10% per annum. What will be the annual installment (X) that the owner has to pay every year to discharge his debt?

  1. Rs. 24,000

  2. Rs. 26,000

  3. Rs. 27,500

  4. Rs. 28,700

  5. Rs. 24,700
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The total amount to be repaid is 1,19,600. With simple interest at 10% over 4 years, the annual installment X is calculated using the formula for installment with simple interest: P = X * n + (X * r * n * (n-1)) / (2 * 100). Solving for X with P=119600, n=4, r=10 gives X = 26,000.

Multiple choice

A certain sum of money, when invested for 5 years at an annual simple interest rate of 6%, yields an amount that exceeds the amount obtained by investing the same principal at an annual compound interest rate of 10% over 2 years by Rs. 900. Determine the principal amount.

  1. Rs. 8,000

  2. Rs. 9,000

  3. Rs. 10,000

  4. Rs. 10,500

  5. Rs. 11,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be the principal. SI = P * 0.06 * 5 = 0.3P. CI = P * (1.10^2 - 1) = 0.21P. Difference = 0.3P - 0.21P = 0.09P. 0.09P = 900, so P = 10000.

Multiple choice

Alex allocated two identical investments of Rs. 5,000 each into two distinct savings accounts for a duration of 2 years. Account X accrues simple interest at an annual rate of 8%, while Account Y compounds interest yearly at an annual rate of 10%. What is the approximate difference between the final values of these investments upon maturation?

  1. Rs. 470

  2. Rs. 480

  3. Rs. 390

  4. Rs. 250

  5. Rs. 210
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Account X (simple interest) yields 5000 * 0.08 * 2 = 800, total 5800. Account Y (compound interest) yields 5000 * (1.10)^2 = 6050. The difference is 6050 - 5800 = 250.

Multiple choice

Anita invested a portion of her savings in a bond with a simple interest rate, and the rest in a savings account with compound interest. The simple interest investment grew to Rs. 9,600 after 4 years with an annual interest rate of 7%. Simultaneously, the compound interest investment, compounded annually at a rate of 10%, grew to Rs. 7,986 after the same period of 3 years. Determine the total amount Anita initially invested in both investments.

  1. Rs. 12,500

  2. Rs. 13,500

  3. Rs. 13,800

  4. Rs. 14,500

  5. Rs. 15,200
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simple interest: P1 * (1 + 0.07 * 4) = 9600 => P1 * 1.28 = 9600 => P1 = 7500. Compound interest: P2 * (1 + 0.10)^3 = 7986 => P2 * 1.331 = 7986 => P2 = 6000. Total = 7500 + 6000 = 13500.

Multiple choice

John is planning to save for his daughter's college education. He decides to invest $10,000 in a fixed deposit account that offers an annual simple interest rate of 8.5%. He plans to leave the money in the account for 6 years. What will be the total amount in the account after 6 years?
  1. $22,100
  2. $18,100
  3. $16,100
  4. $15,100
  5. $14,500
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple interest = (Principal * Rate * Time) / 100 = (10000 * 8.5 * 6) / 100 = 100 * 51 = 5100. Total amount = 10000 + 5100 = 15100.

Multiple choice

Henry deposited two equal sums in two different banks, in the first bank at a simple interest rate for two years and in other bank at compound interest rate for two years. The difference between the compound interest and simple interest on deposits calculated at the same annual interest rate, was \$25. During the same period, the simple interest earned totals \$250. What is the annual rate of interest at which the deposits were made?

  1. 15%

  2. 18%

  3. 20%

  4. 25%

  5. 30%
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Jessica invested \$5,000 for one year at a simple annual interest rate of 5 percent and invested \$12,000 for one year at an annual interest rate of 7 percent compounded quarterly. What is the approximate total amount of interest that Jessica earned on the two investments?
  1. $800
  2. $1,100
  3. $1,300
  4. $1,500
  5. $1,700
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

SI = 5000 * 0.05 * 1 = 250. CI = 12000 * ((1 + 0.07/4)^4 - 1) = 12000 * ((1.0175)^4 - 1) = 12000 * (1.071859 - 1) = 12000 * 0.071859 = 862.3. Total = 250 + 862.3 = 1112.3, which is approximately 1100.

Multiple choice

Robert invests $500 in a savings account that earns 3% interest compounded annually. At the same time, his friend Sarah invests 600 in a different savings account that earns 2.5% interest compounded annually. After 5 years, what will be the difference in their respective amounts?
  1. $59.25
  2. $79.50
  3. $89.23
  4. $99.21
  5. $100.75
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Robert's amount: 500 * (1.03)^5 = 500 * 1.159274 = 579.64. Sarah's amount: 600 * (1.025)^5 = 600 * 1.131408 = 678.84. Difference: 678.84 - 579.64 = 99.20. Rounding differences lead to 99.21.