Practice Compound Interest in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Interest calculated on both the initial principal and the accumulated interest from previous periods. The formula A=P(1+rn)ntA = P\left(1 + \frac{r}{n}\right)^{nt} gives the amount after tt years, and A=PertA = Pe^{rt} gives the continuously compounded amount.

Simple interest pays you only on your original deposit. Compound interest pays you interest on your interest—your money earns money on the money it already earned. The more frequently you compound, the more you earn, because each tiny interest payment starts earning its own interest sooner. The ultimate limit of compounding more and more frequently is continuous compounding: A=PertA = Pe^{rt}.

Showing a random 20 of 50 problems.

Example 1

easy
For monthly compounding, what is the value of nn?

Example 2

easy
For quarterly compounding, what is the value of nn in A=P(1+r/n)ntA=P(1+r/n)^{nt}?

Example 3

hard
Bank A offers 5.1%5.1\% compounded annually; Bank B offers 5%5\% compounded monthly. Which is better?

Example 4

easy
Compute the balance: P=$1000P = \$1000, r=8%r = 8\%, compounded annually, t=2t = 2 years.

Example 5

hard
An account earns 5%5\% compounded quarterly. What is the effective annual rate?

Example 6

hard
A loan of $5,000\$5{,}000 accrues at 9%9\% compounded monthly. If no payments are made, what is owed after 2 years?

Example 7

medium
$2,500\$2{,}500 is invested at 4%4\% compounded semi-annually for 5 years. Find AA.

Example 8

easy
You deposit $500 at 6%6\% annual interest compounded annually. What is the balance after 1 year?

Example 9

easy
In A=PertA=Pe^{rt}, what does PP represent?

Example 10

medium
Find the amount when $2,000\$2{,}000 is invested at 5%5\% compounded continuously for 4 years.

Example 11

hard
Using the rule of 72, estimate the doubling time at 9%9\% annual interest.

Example 12

challenge
How long until $1000\$1000 doubles at 7%7\% compounded continuously? Use ln⁡2≈0.693\ln 2\approx 0.693.

Example 13

easy
You invest $5,000\$5{,}000 at 6%6\% annual interest compounded quarterly. Find the amount after 3 years.

Example 14

easy
You deposit $1,200\$1{,}200 in a savings account at 4%4\% compounded annually. What is the balance after 5 years?

Example 15

hard
What principal yields $1500 of interest in 5 years at 6%6\% compounded annually?

Example 16

medium
How long does it take for an investment to double at 8%8\% annual interest compounded monthly?

Example 17

easy
Convert an interest rate of 4.5%4.5\% to the decimal rr used in the formula.

Example 18

medium
Find the interest earned (not the total) when $1,500\$1{,}500 is compounded annually at 5%5\% for 4 years.

Example 19

easy
Convert a 5% annual interest rate to the decimal rr used in formulas.

Example 20

hard
What annual interest rate, compounded monthly, is needed to grow $3,000\$3{,}000 to $4,500\$4{,}500 in 6 years?
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