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

Lisa invests $5,000 into a savings account that earns 15% annual interest, compounded annually. What is the least number of full years required for her investment to more than double?

  1. 3 years

  2. 4 years

  3. 5 years

  4. 6 years

  5. 7 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To double the investment, the amount must reach at least $10,000. Using the formula A = P(1+r)^t, we solve 5000(1.15)^t > 10000, which simplifies to (1.15)^t > 2. Since 1.15^4 is approximately 1.75 and 1.15^5 is approximately 2.01, 5 years are required.

Multiple choice

Sarah invested $Y in a special savings account that paid simple interest. The amount grew to \$5,000 after 2 years. Sarah then waited for another 3 years and got a final amount of \$8,000. At what annual interest rate did Sarah invest $Y initially?

  1. 33.33%

  2. 23.30%

  3. 18.0%

  4. 16.0%

  5. 16.5%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simple interest for 3 years (from 5000 to 8000) is 3000. Interest per year = 1000. Principal Y = 5000 - (2 * 1000) = 3000. Rate = (Interest / Principal) * 100 = (1000 / 3000) * 100 = 33.33%.

Multiple choice

Mike invested $3,500 for 4 years at 7% annual interest rate that was compounded annually. How much less interest would he have earned if the money had instead been invested at 7% simple annual interest for 4 years?
  1. $107.79
  2. $120.79
  3. $148.20
  4. $156.45
  5. $164.50
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Compound interest = 3500 * (1 + 0.07)^4 - 3500 = 3500 * 1.310796 - 3500 = 1087.786. Simple interest = 3500 * 0.07 * 4 = 980. Difference = 1087.79 - 980 = 107.79.

Multiple choice

David invested \$8,000 for one year in an account that compounds interest semi-annually. He wants to earn at least \$1,245 in interest. What is the minimum annual interest rate, compounded semi-annually, that would achieve his goal?

  1. 15%

  2. 18%

  3. 18.5%

  4. 19%

  5. 19.5%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Interest = P * (1 + r/200)^2 - P. 1245 = 8000 * (1 + r/200)^2 - 8000. 9245 = 8000 * (1 + r/200)^2. 1.155625 = (1 + r/200)^2. sqrt(1.155625) = 1.075. 1 + r/200 = 1.075. r/200 = 0.075. r = 15%.

Multiple choice

Rachel wants to invest in a bond that pays an annual interest rate of 5%, compounded semi-annually. She wants her investment to be at least $3,000 at the end of 2 years. What is the minimum value of her initial investment?
  1. $2,564.50
  2. $2,581.70
  3. $2,602.50
  4. $2,717.85
  5. $2,660.80
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Compound interest formula: A = P(1 + r/n)^(nt). 3000 = P(1 + 0.05/2)^(2*2) = P(1.025)^4. 3000 = P(1.10381289). P = 3000 / 1.10381289 = 2717.85.

Multiple choice

Jessica made a deposit of \$7,500 at a 5% simple annual rate of interest. She also deposited another \$12,800 at a 4% annual rate of interest that was compounded quarterly. What was the approximate total amount of interest rounded to the nearest hundred that Jessica earned from these two deposits after 1 year?
  1. $900
  2. $1,000
  3. $1,200
  4. $1,400
  5. $1,700
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Interest 1: 7500 * 0.05 * 1 = 375. Interest 2: 12800 * (1 + 0.04/4)^4 - 12800 = 12800 * (1.01)^4 - 12800 = 12800 * 1.040604 - 12800 = 519.73. Total interest = 375 + 519.73 = 894.73. Rounded to the nearest hundred, this is 900.

Multiple choice

Emma deposits $2,000 in a bank account that offers an annual simple interest rate of 5%. How much interest will she earn in 2 years, and what will be the total amount in her account at the end of 2 years?
  1. Interest: $150; Total amount: $2,150
  2. Interest: $200; Total amount: $2,200
  3. Interest: $210; Total amount: $2,210
  4. Interest: $250; Total amount: $2,250
  5. Interest: $260; Total amount: $2,260
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simple Interest = P * R * T = 2000 * 0.05 * 2 = 200. Total amount = Principal + Interest = 2000 + 200 = 2200.

Multiple choice

Emily deposits $3,500 into a bank account offering 4% annual simple interest. However, she decides to withdraw half the amount after 2 years. How much interest will she have earned by then, and what is the total balance in her account after this withdrawal?
  1. Interest: \$140; Total balance after withdrawal: \$1,820
  2. Interest: \$240; Total balance after withdrawal: \$1,870
  3. Interest: \$260; Total balance after withdrawal: \$1,880
  4. Interest: \$280; Total balance after withdrawal: \$1,890
  5. Interest: \$300; Total balance after withdrawal: \$1,900
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Emma and Noah are both investing in a sustainable energy initiative. Emma invests \$15,000 for 3 years at a fixed interest rate of 10% per annum. Meanwhile, Noah invests the same amount, \$15,000, for 3 years but divides his investment into three different parts in the ratio 3 : 5 : 7, earning interest rates of 8%, 10%, and x%, respectively. It is known that the total interest earned by Noah is 5% less than the interest earned by Emma. What is the value of x?

  1. 10.79%

  2. 9.79%

  3. 8.45%

  4. 7.83%

  5. 5.84%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Emma's interest = 15000 * 0.10 * 3 = 4500. Noah's interest = 4500 * 0.95 = 4275. Noah's investment parts: 3k+5k+7k = 15k = 15000, so k=1000. Parts are 3000, 5000, 7000. Interest = 3000*0.08*3 + 5000*0.10*3 + 7000*x*3 = 4275. 720 + 1500 + 21000x = 4275. 21000x = 2055. x = 2055/21000 = 0.097857... or 9.79%.