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

Directions: Type in your answer in the input box provided below the question. Joshua took a loan of ₹67100 from a moneylender at 20% per annum under compound interest, compounded annually, and agreed to repay it in four equal annual installments, instalment being paid at the end of each year. Find the value of each installment.

  1. 25920

  2. 14650

  3. 750

  4. 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the formula for equal annual installments P = X / (1+r) + X / (1+r)^2 + X / (1+r)^3 + X / (1+r)^4, where r=0.20 and P=67100. Solving for X gives 25920.

Multiple choice

Steve deposited $100 to open a savings account. If there are no other transactions in the account, what amount of money would the account accrue in 6 months after opening the account? (1) The interest rate is 4%. (2) Interest is compounded quarterly.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To calculate the accrued amount, we need both the interest rate (Statement 1) and the compounding frequency (Statement 2) to determine the effective interest over 6 months.

Multiple choice

Directions: Select the correct alternative from the given choices. If the principal at the beginning of the fifth year on a certain sum at a certain rate of interest, compounded annually, is 20% more than that at the beginning of the fourth year, then by what percent does the compound interest for the eleventh year exceed the compound interest for the eighth year?

  1. 44%

  2. 72.8%

  3. 69%

  4. 61.6%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Principal at start of year 5 is 1.2 * Principal at start of year 4, so rate r = 20% (0.2). CI for year n = P * (1+r)^(n-1) * r. CI for year 11 = P * (1.2)^10 * 0.2. CI for year 8 = P * (1.2)^7 * 0.2. Ratio = (1.2)^10 / (1.2)^7 = (1.2)^3 = 1.728. Increase = 72.8%.

Multiple choice

Directions: Select the correct alternative from the given choices. A certain sum lent at a certain rate of interest per annum, under simple interest, becomes 1.375 times itself in three years. After how many years will the total interest accrued be equal to twice the sum?

  1. 14

  2. 16

  3. 17

  4. 19
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sum becomes 1.375S in 3 years, so interest = 0.375S. Rate = (0.375S * 100) / (S * 3) = 12.5% per annum. To have interest = 2S, 2S = (S * 12.5 * T) / 100. T = 200 / 12.5 = 16 years.

Multiple choice

Directions: Select the correct alternative from the given choices. If a certain sum, invested under compound interest, amounts to twice as much at the end of the seventh year as it would at the end of the second year, then the amount at the end of the 64th year will be how many times that at the end of the 49th year?

  1. 8

  2. 16

  3. 32

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

In compound interest, A = P(1+r)^n. A7 = P(1+r)^7, A2 = P(1+r)^2. A7 = 2 * A2 implies (1+r)^5 = 2. We want A64 / A49 = P(1+r)^64 / P(1+r)^49 = (1+r)^15 = ((1+r)^5)^3 = 2^3 = 8.

Multiple choice

A couple wishes to purchase a house for Rs. 15,00,000 with a down payment of Rs. 4,00,000. If they can amortize the balance at an interest rate 9% per annum compounded monthly for 10 years, find the monthly installment (EMI). [Given, (1.0075)-120 = 0.4079]

  1. Rs. 5324.5

  2. Rs. 15324.5

  3. Rs. 13933.5

  4. Rs. 23933.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Loan amount = 15,00,000 - 4,00,000 = 11,00,000. Interest rate = 9% / 12 = 0.75% per month. n = 120 months. EMI = P * r * (1+r)^n / ((1+r)^n - 1). Using given (1.0075)^-120 = 0.4079, EMI = 1100000 * 0.0075 / (1 - 0.4079) = 8250 / 0.5921 = 13933.45.

Multiple choice

A sum of Rs. 50,000 is lent partly at 4% and remaining at 5% per annum. If the yearly simple interest on the average is 4.6%, the two parts are:

  1. Rs. 22,500, Rs. 27,500

  2. Rs. 15,000, Rs. 35,000

  3. Rs. 20,000, Rs. 30,000

  4. Rs. 25,000, Rs. 25,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using alligation: Part 1 at 4%, Part 2 at 5%, Average at 4.6%. The ratio of parts is (5 - 4.6) : (4.6 - 4) = 0.4 : 0.6 = 2 : 3. Total parts = 5. Each part = 50,000 / 5 = 10,000. Parts are 20,000 and 30,000.

Multiple choice

Quantity A Rate per annum when simple interest on a certain sum is a quarter of the sum in 4 years Quantity B Percentage by which 8.5 is more than 8

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity A: SI = P/4, T = 4. SI = (P * R * T) / 100 => P/4 = (P * R * 4) / 100 => 1/4 = 4R/100 => R = 100/16 = 6.25%. Quantity B: (8.5 - 8) / 8 = 0.5 / 8 = 1/16 = 6.25%. Both are 6.25%.