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

What is the annual interest rate on a loan that has a monthly payment of \$1000, a loan term of 30 years, and a total amount borrowed of \$100,000?

  1. $$4\%$$
  2. $$4.5\%$$
  3. $$5\%$$
  4. $$5.5\%$$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The annual interest rate on a loan that has a monthly payment of \$1000, a loan term of 30 years, and a total amount borrowed of \$100,000 is $$4.5\%$$. This means that the borrower will pay a total of $135,000 in interest over the life of the loan.

Multiple choice

What is the total amount of interest paid on a loan of $100,000 that is repaid over 30 years at an annual interest rate of 5%? (Assume continuous compounding.)

  1. $$\$100,000$$
  2. $$\$135,000$$
  3. $$\$170,000$$
  4. $$\$205,000$$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The total amount of interest paid on a loan of $100,000 that is repaid over 30 years at an annual interest rate of 5% (assuming continuous compounding) is $$\$135,000$$. This means that the borrower will pay a total of $235,000 over the life of the loan.

Multiple choice

What is the present value of an annuity that pays $1000 per year for 10 years at an annual interest rate of 4%? (Assume continuous compounding.)

  1. $$\$8110.90$$
  2. $$\$8203.46$$
  3. $$\$8298.17$$
  4. $$\$8395.13$$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The present value of an annuity that pays $1000 per year for 10 years at an annual interest rate of 4% (assuming continuous compounding) is $$\$8203.46$$. This means that the present value of the annuity is $8203.46.

Multiple choice

What is the future value of an annuity that pays $1000 per year for 10 years at an annual interest rate of 6%? (Assume continuous compounding.)

  1. $$\$12155.06$$
  2. $$\$12387.65$$
  3. $$\$12624.80$$
  4. $$\$12866.51$$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The future value of an annuity that pays $1000 per year for 10 years at an annual interest rate of 6% (assuming continuous compounding) is $$\$12387.65$$. This means that the future value of the annuity is $12387.65.

Multiple choice

What is the present value of a perpetuity that pays $1000 per year at an annual interest rate of 5%? (Assume continuous compounding.)

  1. $$\$20,000$$
  2. $$\$25,000$$
  3. $$\$30,000$$
  4. $$\$35,000$$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The present value of a perpetuity that pays $1000 per year at an annual interest rate of 5% (assuming continuous compounding) is $$\$20,000$$. This means that the present value of the perpetuity is $20,000.

Multiple choice

A sum of money doubles itself in 10 years at a certain rate of simple interest. In how many years will it triple itself at the same rate of interest?

  1. 15 years

  2. 20 years

  3. 25 years

  4. 30 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the sum of money be (\$P) and the rate of interest be (\$r)%. Then, the amount after 10 years is (\$P + P \times r \times 10/100 = 2P). Therefore, (\$r = 10)%. Now, let the number of years required for the sum to triple itself be (\$n). Then, the amount after (\$n) years is (\$P + P \times r \times n/100 = 3P). Substituting (\$r = 10)%, we get (\$3P = P + P \times 10 \times n/100). Simplifying, we get (\$n = 15) years.

Multiple choice

Which of the following is an example of a compounding interest scenario?

  1. Saving money in a bank account that earns interest

  2. Taking out a loan with a fixed interest rate

  3. Investing in a stock that pays dividends

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Compounding interest occurs when interest is earned on both the principal amount and the accumulated interest. Saving money in a bank account, taking out a loan with a fixed interest rate, and investing in a stock that pays dividends are all examples of compounding interest scenarios.

Multiple choice

What is the effect of compounding interest on the growth of money over time?

  1. It accelerates the growth of money

  2. It slows down the growth of money

  3. It has no effect on the growth of money

  4. It depends on the interest rate
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Compounding interest has a significant impact on the growth of money over time. Due to the reinvestment of interest earned, the money grows at an exponential rate, leading to accelerated growth compared to simple interest.

Multiple choice

A company has a loan of \$100,000 with an annual interest rate of 5%. If the company makes monthly payments of \$1,000, how long will it take to pay off the loan?

  1. 10 years

  2. 15 years

  3. 12 years

  4. 8 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The monthly interest rate is 5% / 12 = 0.42%. The monthly payment is \$1,000. The loan amount is \$100,000. Using the formula for the number of months to pay off a loan: Number of months = (Loan amount * Monthly interest rate) / Monthly payment, we get Number of months = (\$100,000 * 0.0042) / \$1,000 = 144 months. Therefore, it will take 144 / 12 = 12 years to pay off the loan.

Multiple choice

What is the formula for calculating the effective annual interest rate (EAR) from the nominal annual interest rate (r) and the number of compounding periods (m)?

  1. EAR = (1 + r/m)^m - 1

  2. EAR = (1 - r/m)^m - 1

  3. EAR = (1 + r*m)^m - 1

  4. EAR = (1 - r*m)^m - 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The effective annual interest rate (EAR) is calculated using the formula EAR = (1 + r/m)^m - 1, where r is the nominal annual interest rate and m is the number of compounding periods.

Multiple choice

What is the relationship between the effective annual interest rate (EAR) and the nominal annual interest rate (r) when the interest is compounded continuously?

  1. EAR = e^r - 1

  2. EAR = e^-r - 1

  3. EAR = (e^r)^m - 1

  4. EAR = (e^-r)^m - 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When the interest is compounded continuously, the effective annual interest rate (EAR) is calculated using the formula EAR = e^r - 1, where r is the nominal annual interest rate.

Multiple choice

A farmer is considering two different loan options, A and B. Loan A has an interest rate of 5% and a repayment period of 10 years. Loan B has an interest rate of 6% and a repayment period of 5 years. If the farmer needs to borrow $100,000, which loan should the farmer choose?

  1. Loan A

  2. Loan B

  3. Both loans have the same total cost

  4. Cannot be determined from the given information
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total cost of Loan A is $100,000 * (1 + 0.05)^10 - $100,000 = \$162,889.46. The total cost of Loan B is \$100,000 * (1 + 0.06)^5 - $100,000 = $133,822.58. Therefore, Loan A has the lower total cost and should be chosen by the farmer.

Multiple choice

A sum of money was invested in a bank at 6% p.a. simple interest for 2 years. If it had been invested in mutual fund at the rate of 8% p.a. simple interest for 4 years, then the earnings would have been Rs. 1000 more. What was the sum invested?

  1. Rs. 4500

  2. Rs. 5000

  3. Rs. 3500

  4. Rs. 5500

  5. Rs. 6000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let sum be P. Interest 1 = P * 0.06 * 2 = 0.12P. Interest 2 = P * 0.08 * 4 = 0.32P. Difference = 0.32P - 0.12P = 0.20P = 1000. P = 1000 / 0.20 = 5000.

Multiple choice

A father left a will that his capital of Rs. 18,750 be divided between his two sons, aged 12 and 14 years, such that when they attain the age of 18 years, the amounts received by each at 5% simple interest are the same. Find the sum allotted to the elder son.

  1. Rs. 9750

  2. Rs. 9450

  3. Rs. 9000

  4. Rs. 8700
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be the amount for the elder son (14 years old) and (18750-x) for the younger (12 years old). Elder son's money grows for 4 years, younger for 6 years. x(1 + 0.05*4) = (18750-x)(1 + 0.05*6). x(1.2) = (18750-x)(1.3). 1.2x = 24375 - 1.3x. 2.5x = 24375 => x = 9750.

Multiple choice

The compound interest accrued on an amount of Rs. 18,000 at the end of three years is Rs. 5,958. What would be the simple interest accrued on the same amount at the same rate in the same period?

  1. Rs. 5,100

  2. Rs. 5,400

  3. Rs. 5,700

  4. Rs. 4,800

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

For 3 years, CI = P((1+r)^3 - 1) = 5958. With P=18000, (1+r)^3 - 1 = 5958/18000 = 0.331. Thus (1+r)^3 = 1.331, so 1+r = 1.1 and r = 10%. Simple interest for 3 years at 10% is 18000 * 0.1 * 3 = 5400.