Compound Interest Calculator
Variable Key
Compound interest formula
Standard formula for periodic compounding.
Continuous compounding
Limit as compounding frequency → ∞.
Find principal
How much to invest today to reach a goal.
Find rate
What annual rate is needed?
Rule of 72
Approximate years to double at a given rate.
Compound interest calculates interest on both the initial principal and the previously accumulated interest. Unlike simple interest (which only grows on the principal), compound interest grows exponentially — your interest earns interest. Einstein reportedly called it "the eighth wonder of the world."
Tip: The frequency of compounding matters most at higher rates. At 1%, daily vs annual compounding adds almost nothing. At 10%, it adds $47 per $1,000 per year.
- 1Start with your principal amount P
- 2Determine the annual rate r and how often it compounds (n times per year)
- 3Apply the formula: A = P(1 + r/n)^(nt)
- 4The difference A − P is the total interest earned
Rule of 72
Divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6%: 72÷6 = 12 years.
Continuous compounding
The theoretical maximum — compounding every instant. Formula: A = Pe^(rt). At 5% for 10 years: $1,648.72.
| Rate | Years to double | Exact years |
|---|---|---|
| 1% | 72 | 69.66 |
| 2% | 36 | 35.00 |
| 3% | 24 | 23.45 |
| 4% | 18 | 17.67 |
| 5% | 14.4 | 14.21 |
| 6% | 12 | 11.90 |
| 7% | 10.3 | 10.24 |
| 8% | 9 | 9.01 |
| 10% | 7.2 | 7.27 |
| 12% | 6 | 6.12 |
Fun Fact
If you had put $1 in a bank in the year 1 AD at 5% compound interest, by the year 2000 it would be worth more than all the gold ever mined on Earth.