The compound interest formula
For a single deposit, the future value is:
A = P × (1 + r/n)n × t
where P is the starting amount, r the annual rate as a decimal, n the number of compounding periods per year and t the number of years. Regular contributions are added as a series of monthly deposits (an annuity), each growing for the time remaining:
FVcontributions = C × ((1 + i)m − 1) ÷ i
Here C is the monthly contribution, m the number of months and i the monthly growth rate equivalent to your compounding choice. Contributions are assumed at the end of each month.
Example: You invest $10,000 and add $200 every month for 20 years at 7% compounded monthly. You deposit $58,000 in total and end with about $144,573 — more than $86,500 of it is interest.
Why time matters more than anything else
In the example above, the balance after 10 years is about $54,700. The second decade adds almost $90,000 because interest is now being earned on a much larger base. Starting early — even with small amounts — usually beats contributing more later.
Where compound interest applies
- High-yield savings accounts and CDs — usually compounded daily or monthly.
- Bonds and bond funds — interest reinvested compounds over time.
- Stock index funds — returns are not guaranteed, but reinvested dividends and growth compound in a similar way. Using a long-run average return (for example 6–8% before inflation) gives a rough projection.
- Debt — credit cards compound against you. See the credit card payoff calculator.
Frequently asked questions
What is compound interest?
Compound interest is interest earned on both your original deposit and the interest already added to it. Because the base keeps growing, the balance grows faster each year than it would with simple interest.
How often should interest compound?
More frequent compounding produces slightly more growth, but the effect is small at typical rates. $10,000 at 7% for 20 years grows to $38,697 with annual compounding, $40,387 with monthly compounding and $40,547 with daily compounding. The rate and the time invested matter far more.
What is the Rule of 72?
Divide 72 by the annual interest rate to estimate how many years it takes money to double. At 6%, money doubles in about 12 years; at 9%, about 8 years. It is an approximation that works best for rates between 4% and 12%.
What is the difference between APR and APY?
APR is the nominal annual rate. APY (annual percentage yield) includes the effect of compounding. A 5% APR compounded monthly equals an APY of about 5.12%. The calculator shows this as the “effective annual rate”.
Does this include taxes or inflation?
No. Results are before taxes and in nominal dollars. To see what a future balance is worth in today’s money, use the inflation calculator.