How to Calculate Compound Interest: Formula, Examples & Calculator
A plain-English guide to compound interest — the formula, worked examples with real numbers, and why starting early makes such a disproportionate difference.
Simple Interest vs Compound Interest
Simple interest is calculated only on your original principal. If you deposit $5,000 at 6% simple interest, you earn $300 every year — the same amount, year after year.
Compound interest is calculated on your principal plus any interest already earned. In year one you earn $300. In year two, you earn 6% on $5,300 — which is $318. In year three, you earn 6% on $5,618. The base keeps growing, and so does the amount you earn.
Over long periods, this difference becomes enormous. At 6% over 30 years, $5,000 simple interest grows to $14,000. At 6% compounded annually, it grows to $28,717 — more than double.
The Compound Interest Formula
A = P(1 + r/n)^(nt)
Where: A = final amount, P = principal (starting amount), r = annual interest rate as a decimal (6% = 0.06), n = number of times interest compounds per year, t = time in years.
For annual compounding, n = 1. For monthly compounding, n = 12. For daily compounding, n = 365.
Worked Example: Annual vs Monthly Compounding
Starting amount: $5,000. Annual rate: 6%. Time: 10 years.
Annual compounding (n = 1): A = 5,000 × (1 + 0.06/1)^(1×10) = 5,000 × (1.06)^10 = $8,954
Monthly compounding (n = 12): A = 5,000 × (1 + 0.06/12)^(12×10) = 5,000 × (1.005)^120 = $9,097
Monthly compounding produces an extra $143 over 10 years — not dramatic at this scale, but the gap widens with larger amounts and longer time horizons.
Why Time Is the Most Powerful Variable
Of all the variables in the formula — rate, compounding frequency, contribution amount — time has the most dramatic effect. The reason is that compound growth is exponential, not linear. The growth you earn in year 25 is far larger than the growth you earn in year 5, even with identical contributions.
| Years invested | Final value (6%, monthly) | Total growth |
|---|---|---|
| 10 years | $9,097 | +82% |
| 20 years | $16,551 | +231% |
| 30 years | $30,136 | +503% |
| 40 years | $54,855 | +997% |
The Rule of 72
A quick mental shortcut: divide 72 by your annual interest rate to estimate how many years it takes to double your money.
At 6%: 72 ÷ 6 = 12 years. At 8%: 9 years. At 4%: 18 years.
This rule works because 72 is a reasonable approximation of 100 × ln(2) ≈ 69.3, adjusted upward for divisibility. It is accurate to within a year or two for most typical interest rates.
Use our Rule of 72 Calculator to see exact doubling times for any rate.
Calculate Compound Interest
Use our free Compound Interest Calculator to model any combination of principal, rate, compounding frequency, time, and monthly contributions — and see a full breakdown of contributions versus interest earned.
Enter a principal, rate, and time period to see exactly how compound interest grows your money.
Compound Interest Calculator →