How compound interest works
Compound interest means each period’s interest is added to the balance and then earns interest itself. Monthly compounding divides the annual rate by 12 and applies it each month, so growth compounds 12 times per year rather than once.
Worked example. Deposit $1,000 at 5% per year, compounding monthly, and leave it for 10 years. The future value is roughly $1,647 — $647 in interest on a $1,000 investment, just from leaving it alone.
The formula
Monthly rate r = annualRate / 12. After n = years × 12 months:
- Future value of principal =
principal × (1 + r)^n - Future value of monthly contributions =
contribution × ((1 + r)^n − 1) / r
Total future value is the sum of both.
Why time is the biggest lever
Doubling the rate has less impact than doubling the time period, especially in early years. Starting at 25 versus 35 with the same monthly contribution can mean hundreds of thousands of dollars by retirement — this is why the rule of thumb is “start early, even small.”