How Compound Interest Works Over Time
Compounding keeps each year's interest in the account so it earns interest too. The tool compounds once a year and raises 1 + rate to the number of years.
Open the tool：Compound Interest Calculator
Time does most of the work
10,000 at 5% for 10 years becomes about 16,289, with 6,289 of interest, a multiple of 1.63. Leave the same money for 30 years and it reaches about 43,219, or 4.32 times. The rate did not change; the extra 20 years did the work, which is the part people underestimate most.
Use it to compare products, to sanity-check a projection, or to see what a child's education fund could become over two decades. It also answers the reverse question: doubling in 10 years needs about 7.18% a year, which the rule of 72 rounds to 7.2%.
- Project a single lump sum
- Compare long-run outcomes at different rates
- Sanity-check a doubling-time claim
Annual compounding and the inputs
Final value = principal × (1 + rate)^years. Enter 5 for 5%, not 0.05. Compounding is fixed at once a year. Fractional years are allowed and are evaluated as a real exponent, which is a smooth interpolation rather than monthly or semi-annual compounding.
The result ignores subscription fees, management fees, custody fees, tax and inflation, so the money you keep is usually less. Interest = final − principal and multiple = final ÷ principal, each rounded to two decimals, so the three figures can differ by a cent.
- Rate as 5, not 0.05
- Compounding is annual only
- Fees, tax and inflation are excluded
Real returns are messier
Products compound on different schedules: monthly compounding produces a higher effective annual rate than the same nominal rate compounded annually, and daily is higher still. Bond coupons introduce reinvestment questions. Annual compounding is the conservative case.
The tool handles one lump sum only: no monthly contributions, withdrawals or reinvested dividends. For those, use a cash-flow or IRR calculator. To compare funds, use returns net of fees, not the headline seven-day or since-inception figure.
- Regular contributions need a cash-flow tool
- Compare net-of-fee returns
- Long horizons magnify a wrong rate assumption
FAQ
Why is this lower than my banking app?
The app may compound monthly or daily, and may reinvest paid interest immediately. This tool compounds once a year, charges nothing and assumes no extra deposits. Monthly compounding at the same nominal rate gives an effective rate of (1 + r/12)^12 − 1, slightly above the nominal figure.
Is the rule of 72 accurate?
It is a mental shortcut: 72 ÷ rate approximates the doubling time. At 5% it suggests 14.4 years, while ln 2 ÷ ln 1.05 is about 14.2. At 8% it gives 9 years against an exact 9.01, so the error stays small at common rates.
Do fractional years make sense?
Only as a rough interpolation. The tool raises 1 + rate to a real exponent, which assumes smooth growth within the year. Real products may pay monthly, quarterly or at maturity, so whole years are closer to how they actually behave.
Related tool：Compound Interest Calculator