Lesson 5 of 10
Compound interest
Compound interest adds earlier interest to the base that earns the next period’s interest.
The idea
Compounding means that retained interest can itself earn interest. With a constant annual rate r, principal P, n compounding periods per year, and t years, the illustrative ending balance is P × (1 + r/n)^(n×t).
Frequency changes the result when the quoted rate is nominal and interest remains in the account. Do not confuse a nominal annual rate with an annual percentage yield. A constant positive rate is a scenario assumption, not a forecast of investment returns.
Worked example
Original arithmetic example: Begin with $1,000 at 10% annually, compounded once per year. Year 1 adds $100, reaching $1,100. Year 2 adds $110, reaching $1,210. The extra $10 compared with simple interest is interest earned on the first year’s $100.
| Year | Opening amount | Interest | Ending amount |
|---|---|---|---|
| 1 | $1,000 | $100 | $1,100 |
| 2 | $1,100 | $110 | $1,210 |
A common mistake
Reading a smooth illustrative growth line as a guarantee that market investments rise every year.
Try it yourself
Start with $2,000 at a hypothetical 5% annual rate for two years, compounded annually, with no contributions. Calculate each year separately.
Show the worked answer
Year 1: $2,100. Year 2: $2,205. Total growth: $205. Simple interest would have produced $2,200.