Compound Interest Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

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

Solution

  1. 1
    Use the formula A=P(1+rn)ntA = P\left(1 + \frac{r}{n}\right)^{nt} with P=5000P = 5000, r=0.06r = 0.06, n=4n = 4, t=3t = 3.
  2. 2
    Substitute: A=5000(1+0.064)4โ‹…3=5000(1.015)12A = 5000\left(1 + \frac{0.06}{4}\right)^{4 \cdot 3} = 5000(1.015)^{12}.
  3. 3
    Compute (1.015)12โ‰ˆ1.19562(1.015)^{12} \approx 1.19562, so Aโ‰ˆ5000ร—1.19562โ‰ˆ5978.09A \approx 5000 \times 1.19562 \approx 5978.09.

Answer

Aโ‰ˆ$5,978.09A \approx \$5{,}978.09
Compound interest applies the interest rate multiple times per year. The key parameters are the principal PP, annual rate rr, compounding frequency nn, and time in years tt.

About Compound Interest

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.

Learn more about Compound Interest โ†’

More Compound Interest Examples

Example 2 medium

How long does it take for an investment to double at [formula] annual interest compounded monthly?

Example 3 medium

Find the amount when [formula]2{,}000[formula]5%$ compounded continuously for 4 years.

Example 4 easy

You deposit [formula]1{,}200[formula]4%$ compounded annually. What is the balance after 5 years?

Example 5 hard

What annual interest rate, compounded monthly, is needed to grow [formula]3{,}000[formula][formula]

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