Last updated May 2026
“Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it.”
attributed to Albert Einstein (apocryphal but widely cited)
The formula.
A = P × (1 + r/n)^(n × t)
A is the future value (what you'll owe or accumulate). P is the principal (the starting amount). r is the annual rate as a decimal. n is how many times per year compounding happens (12 for monthly, 365 for daily). t is years.
The exponent, n × t, is what makes compounding exponential. Linear growth (a flat fee) just multiplies. Exponential growth raises to a power.
For typical U.S. consumer loans, n = 12 (monthly compounding). This is standard for auto loans, mortgages, and credit cards.
What that math actually costs.
Take a $400,000 balance at 7% APR. Cumulative interest paid over time:
| Years held | Cumulative interest |
|---|---|
| 1 year | $7,000 |
| 5 years | $40,255 |
| 10 years | $96,715 |
| 15 years | $175,884 |
| 20 years | $286,968 |
| 30 years | $558,040 |
By year 30, you've paid more in interest than the original $400,000 loan. The growth is non-linear. Each year compounds harder than the previous one.
The Rule of 72.
Divide 72 by the rate to estimate how many years it takes for cost to double. At 7% APR, the interest expense roughly doubles every 10.3 years. At 12%, it doubles every 6 years. At 18% (subprime auto), it doubles every 4 years.
The Rule of 72 is approximate (not exact) but it's how professional finance people quickly estimate compounding. It works for any compound rate.
For a flat fee, there is no doubling rule. The fee is the fee.