Money calculations
How to calculate compound interest
Compound interest is calculated on the starting principal and on interest already added. The balance grows faster than with simple interest because each new period starts from a larger amount.
Open the compound interest calculatorA = P(1 + r ÷ n)nt
A is the final amount, P the principal, r the annual rate as a decimal, n compounds per year, and t years.
Work through the formula
Suppose $5,000 earns 6% annually for 4 years, compounded monthly.
- Convert 6% to a decimal: r = 0.06.
- Monthly compounding means n = 12.
- There are 12 × 4 = 48 compounding periods.
- Calculate $5,000(1 + 0.06 ÷ 12)48 = $6,352.45, rounded to cents.
The compound interest earned is final amount minus principal: $6,352.45 − $5,000 = $1,352.45.
| Input | Value |
|---|---|
| Principal | $5,000 |
| Annual rate | 6% |
| Frequency | Monthly |
| Time | 4 years |
How compounding frequency changes growth
With the same stated annual rate, more frequent compounding usually produces a slightly larger amount because interest is added sooner. Annual compounding uses n = 1, quarterly uses 4, monthly uses 12, and daily commonly uses 365.
Do not confuse a nominal annual rate with an effective annual rate. The effective rate includes intra-year compounding. For a 6% nominal rate compounded monthly, the effective annual rate is (1 + 0.06 ÷ 12)12 − 1, about 6.17%.
Regular contributions need a second calculation
If you add money each month, every contribution compounds for a different length of time. A contribution made at the start of a period earns one more period of interest than one made at the end. Confirm which timing a calculator assumes.
Fees, taxes, changing rates, withdrawals and irregular deposits are not part of the basic formula. For projections, use the rate and schedule that match the account terms, and treat the answer as an estimate rather than a promised return.
Common calculation errors
- Using 6 instead of 0.06 for a 6% rate.
- Using months for time while leaving the rate annual.
- Forgetting that the exponent is the total number of periods.
- Rounding the periodic rate or balance after every step.
Keep full precision until the final displayed result.
Calculate compound growth online
Use the free Compound Interest Calculator to enter principal, annual rate, compounding frequency and time. It shows the estimated final balance and interest earned. This is general informational math, not financial advice.