Formula
A = P × (1 + r ÷ n)^(n × t)continuous: A = P × e^(r × t)
- P — starting amount
- r — annual rate as a decimal
- n — compounding periods per year
- t — years
Each period's interest is added to the balance, so the next period earns interest on a bigger amount.
Worked example
10,000 at 5% for 10 years, monthly
- Starting amount
- 10,000
- Interest rate per year
- 5 %
- Time (years)
- 10 years
- Compounded
- Monthly
Final amount
16,470.09
Interest earned: 6,470.09
Effective annual rate: 5.1162%
Growth multiple: 1.647
How it works
10,000 at 5% for 10 years grows to 16,288.95 compounded yearly, 16,470.09 compounded monthly and 16,487.21 compounded continuously. More frequent compounding helps, but with diminishing returns — the jump from yearly to monthly is much bigger than from monthly to daily.
The effective annual rate shows the true yearly growth after compounding, which is what lets you compare accounts that compound at different frequencies. Money added regularly isn't included here — see the SIP Calculator and RD Calculator — and without compounding you'd use the Simple Interest Calculator. To judge growth after inflation use the Inflation Calculator.
Assumptions and limits
- Constant rate; no deposits or withdrawals; taxes aren't deducted.
- Table shows up to the first 100 years.