Compound Interest — Practice Quiz

A Algebra cheat sheet for Compound Interest — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Practice quiz

1. You invest \$5,000 in an account that pays $4.5\%$ annual interest compounded quarterly. What will be the value of your investment after $6$ years? Round to the nearest cent.

   • \$6,539.96
   • \$6,511.30
   • \$6,546.52
   • \$6,350.00

   Answer: \$6,539.96

2. What principal amount must be invested today at an annual interest rate of $3.2\%$ compounded monthly to accumulate \$10,000 in $5$ years? Round to the nearest cent.

   • \$8,523.25
   • \$8,542.83
   • \$8,400.00
   • \$9,375.58

   Answer: \$8,523.25

3. An investment of \$2,500 grows to \$3,500 in an account that compounds interest semi-annually at an annual rate of $6\%$. Approximately how many years did it take for the investment to grow? Round to two decimal places.

   • 5.69 years
   • 5.77 years
   • 6.67 years
   • 5.62 years

   Answer: 5.69 years

4. If you invest \$1,000 and it grows to \$1,300 in $4$ years with interest compounded annually, what is the annual interest rate? Give your answer as a percentage rounded to two decimal places.

   • 6.78\%
   • 7.50\%
   • 30.00\%
   • 2.21\%

   Answer: 6.78\%

5. Calculate the future value of an investment of \$7,500 at an annual interest rate of $2.8\%$ compounded continuously for $10$ years. Round to the nearest cent.

   • \$9,923.47
   • \$9,885.36
   • \$9,923.37
   • \$9,600.00

   Answer: \$9,923.47

6. How much principal must be invested today at an annual interest rate of $5\%$ compounded continuously to reach \$20,000 in $8$ years? Round to the nearest cent.

   • \$13,406.40
   • \$13,536.79
   • \$12,000.00
   • \$13,417.55

   Answer: \$13,406.40

7. An initial investment of \$4,000 grows to \$5,500 with an annual interest rate of $3.5\%$ compounded continuously. How many years did it take for the investment to reach this amount? Round to two decimal places.

   • 9.10 years
   • 10.01 years
   • 10.71 years
   • 9.26 years

   Answer: 9.10 years

8. You have \$1,000 to invest for $5$ years at an annual interest rate of $4\%$. How much more will you earn if the interest is compounded continuously compared to being compounded annually? Round to the nearest cent.

   • \$4.75
   • \$4.34
   • \$1,221.40
   • \$1,216.65

   Answer: \$4.75

9. Which of the following variables in the compound interest formula $A = P\left(1 + \frac{r}{n}\right)^{nt}$ represents the number of times interest is compounded per year?

   • $n$
   • $t$
   • $r$
   • $P$

   Answer: $n$

10. An investment of \$3,000 is made for $7$ years at an annual interest rate of $3\%$. Calculate the difference in the future value if the interest is compounded monthly versus compounded daily (assume $365$ days in a year). Round to the nearest cent.

    • \$0.94
    • \$10.44
    • \$0.03
    • \$3,701.00

    Answer: \$0.94