Compound interest calculator
Enter a starting amount, an optional monthly deposit, the annual rate and the number of years to see the final balance, how much of it is interest, the effective annual rate and how long the money takes to double.
Result
- Final balance
- $16,470.09
- Total deposited
- $10,000.00
- Interest earned
- $6,470.09
- Effective annual rate (APY)
- 5.12%
- Time to double
- 13.9 years
How to use this tool
- Enter the amount you start with and, if you save regularly, the monthly deposit.
- Enter the annual interest rate and how many years the money stays invested.
- Pick how often interest is compounded. Savings accounts are usually monthly or daily.
- Read the final balance and the share of it that is interest; use the doubling time to compare rates quickly.
Good to know
- Deposits are added at the end of each compounding period (an ordinary annuity); for quarterly, annual or daily compounding the monthly deposit is pooled per period.
- The number of compounding periods is rounded to a whole number, so fractional years are most accurate with monthly or daily compounding.
- Total deposited is the starting amount plus every deposit that was compounded (monthly deposit × 12 × years for whole years); interest earned is the final balance minus that figure.
Frequently asked questions
What formula does the calculator use?
The final balance is P × (1 + i)^n + c × ((1 + i)^n − 1) ÷ i, where P is the starting amount, i the rate per compounding period (annual rate ÷ periods per year), n the number of periods and c the deposit per period. $10,000 at 5% compounded monthly for 10 years gives (1 + 0.05 ÷ 12)^120 ≈ 1.6470, so the balance is $16,470.09.
How are monthly deposits handled with quarterly, annual or daily compounding?
Deposits are assumed to arrive at the end of each period, so the monthly amount is pooled per compounding period: a $100 monthly deposit becomes $300 per quarter or $1,200 per year, and about $3.29 per day for daily compounding. This keeps the arithmetic exact for monthly compounding and very close for the others.
What is the effective annual rate?
It is the rate you actually earn over a year once compounding is included: (1 + i)^m − 1, where m is the number of periods per year. A nominal 5% compounded monthly works out to 5.12% effective, and the more often interest is added the higher the effective rate, though the gap between monthly and daily is tiny.
How is the time to double worked out?
It solves (1 + i)^n = 2 for n, which gives ln 2 ÷ (m × ln(1 + i)) years. This counts growth of the starting amount only, ignoring deposits. At 5% compounded monthly money doubles in about 13.9 years, close to the rule of 72 estimate of 72 ÷ 5 = 14.4 years. When the rate is 0% the balance never doubles, so a dash is shown.
Does it account for tax, fees or inflation?
No. The figures are gross, before tax on interest, account fees and inflation. To estimate real purchasing power, subtract the expected inflation rate from the interest rate before you calculate, and remember that banks can change variable rates during the period.
Results are estimates for general information. Double-check anything important with an official source.