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

Charlie and Jennifer each deposited the same amount of money in Pure Point Financial company at compound interest and simple interest respectively, at the same rate of 10% per annum. Charlie earned $310 more than Jennifer by making an investment for a period 3 years. How much amount did each of them invest?
  1. $15,310
  2. $13,300
  3. $12,310
  4. $10,000
  5. $9,600
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P be the principal. Simple interest for 3 years at 10% is 0.3P. Compound interest is P(1.1^3 - 1) = 0.331P. The difference is 0.031P = 310, so P = 310 / 0.031 = 10,000.

Multiple choice

Boston and Willow borrowed same amount from Kimberly Finance at the same rate. Boston borrowed the money for 2 years and he had to pay \$416 including compound interest annually. Willow borrowed the money for 1 year and he had to pay \$400 including simple interest. At what rate percent did they borrow the money?

  1. 4%

  2. 14%

  3. 12%

  4. 8%

  5. 15%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let P be the principal and r be the rate. Willow: P + P*r = 400. Boston: P(1+r)^2 = 416. Dividing these, (1+r) = 416/400 = 1.04. Thus, r = 0.04 or 4%.

Multiple choice

What will be the compound interest on \$6,000 after 3 years? (1) There was a 30% increase in the amount in 6 years at simple interest. (2) The amount of compound interest is less than \$50,000.

  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
A Correct answer
Explanation

Statement 1 gives the rate of simple interest (30% in 6 years = 5% p.a.). With the principal and rate, CI can be calculated. Statement 2 is just a bound and does not define the rate or principal.

Multiple choice

Mr. Baker, who owns a bookstore in Manhattan, invested $40,000 in a corporate bond that assured a minimum return equivalent to an interest rate of 4.25% compounded annually. As the index was good that year, Mr. Baker got double the minimum interest rate. Find the amount of interest earned if Mr. Baker invested the sum for exactly one year.
  1. $1,700
  2. $2,480
  3. $3,400
  4. $3,600
  5. $4,400
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Minimum interest rate is 4.25 percent. Actual rate is 8.5 percent. Interest = 40,000 * 0.085 = 3,400.

Multiple choice

Mr. Brandon, a private financier, loaned a certain amount to Mr. Benjamin for his house renovation at the rate of 5% simple interest. Mr. Benjamin never paid a single penny for five years to Mr. Brandon, and he owed $20,000 worth of interest for those years. How much amount does Mr. Benjamin have to return to Mr. Brandon to clear all his dues?
  1. $80,000.00
  2. $90,000.00
  3. $95,000.00
  4. $100,000.00
  5. $120,000.00
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple interest I = P * R * T / 100. 20,000 = P * 0.05 * 5. 20,000 = 0.25P. P = 80,000. Total amount to return = Principal + Interest = 80,000 + 20,000 = 100,000.

Multiple choice

Mitchel got retired from her services in military and was looking for a best retirement plan to invest her \$24,025. She was offered a couple of plans by Fidelity Investments on different interest rates. She opted for a plan that provides compound interest making her amount to \$27,225 on her amount after 2 years. What was the approximate rate percent offered to Mitchel?

  1. 5.3%

  2. 6.5%

  3. 7.5%

  4. 7.8%

  5. 8%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the compound interest formula A = P(1 + r/100)^n, we have 27225 = 24025(1 + r/100)^2. Dividing both sides by 24025 gives 1.1332 = (1 + r/100)^2. Taking the square root of 1.1332 yields approximately 1.0645, meaning r is approximately 6.5%.

Multiple choice

Gabriel took a home loan of \$75,000 at simple rate of interest. If he paid \$129,000 after some years to clear the loan which was given at 18% rate of interest, then for how many years had he taken the loan?

  1. 4 years

  2. 5 years

  3. 6 years

  4. 7 years

  5. 8 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The interest earned is 129,000 - 75,000 = 54,000. Using the simple interest formula I = P*R*T/100, we have 54,000 = 75,000 * 0.18 * T. Solving for T gives 54,000 / 13,500 = 4 years.

Multiple choice

Charlie invested \$14,000 at 4 percent and Warren invested some amount at 3 percent annual interest. After a year, they earned a total return of \$770 collectively. Quantity A Amount invested by Warren in the beginning of the year Quantity B $7,000

  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

Charlie's interest: 14000 * 0.04 = 560. Total interest is 770, so Warren's interest is 770 - 560 = 210. Warren's principal: 210 / 0.03 = 7000. Quantity A = 7000, Quantity B = 7000.

Multiple choice

Christian obtained a certain amount of loan for the expansion of his business at a simple annual interest rate of 15 percent. After one year, he repaid the loan with a single payment of \$52,325, including the interest. Quantity A Total amount of money that Christian borrowed in the beginning Quantity B \$45,500

  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

A = P(1 + RT/100). 52325 = P(1 + 0.15 * 1) = P(1.15). P = 52325 / 1.15 = 45500. Quantity A = 45500. Quantity B = 45500. They are equal.

Multiple choice

Jack kept \$56,000 in his bank account at simple interest annually. After some years, he received the total amount as \$64,400 including interest. If the rate of interest provided by the bank was 5%, then for how many years did he keep the amount in the bank?

  1. One year

  2. Two years

  3. Three years

  4. Four years

  5. Five years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple interest = Total amount - Principal = 64400 - 56000 = 8400. Using SI = (P * R * T) / 100, we get 8400 = (56000 * 5 * T) / 100. Solving for T gives 8400 = 2800 * T, so T = 3 years.

Multiple choice

Person X wanted to expand his business, so he decided to buy some more land, but fell short of money. So, he went to a moneylender. The moneylender lent him \$16,000 at a simple annual interest rate of r percent. After 2 years, person X made a single payment of \$18,240 to repay the loan, including the interest. What was the value of r?

  1. 5

  2. 6

  3. 7

  4. 8

  5. 10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Interest = 18240 - 16000 = 2240. Simple interest formula: I = PRT/100. 2240 = 16000 * r * 2 / 100. 2240 = 320 * r. r = 2240 / 320 = 7%.

Multiple choice

Nora decided to pay off a debt of $36,000 to CASA Bank by 40 annual installments, in the form of an A.P. When 30 installments had been paid, she died, leaving one third of the debt unpaid. What was the value of the first installment? (Assuming there is no rate of interest)
  1. $450
  2. $470
  3. $490
  4. $510
  5. $600
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the installments be a, a+d, ..., a+39d. Total sum = 36000. Sum of 40 terms = 20(2a + 39d) = 36000. After 30 installments, 1/3 of debt (12000) remains, so 24000 paid. Sum of 30 terms = 15(2a + 29d) = 24000. Solving the system gives a=510.

Multiple choice

Alice lent \$1200 at simple interest for as many years as the rate of interest. What is the rate of interest? (1) She paid \$1632 by the end of the loan period. (2) She paid $432 as simple interest by the end of the loan period.

  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
D Correct answer
Explanation

Simple interest is calculated as I = (P * R * T) / 100. Given P = 1200 and T = R, the formula becomes I = (1200 * R * R) / 100 = 12 * R^2. Both statements provide the value of I (either directly or via the total amount), allowing for the calculation of R.