Investing
How Compound Interest Works: Formula, Examples & Calculator
Compound interest means you earn interest on your original money and on the interest it has already earned. Over long periods, that second part can end up larger than the first.
7 min read
What compound interest is
When interest is added to a balance, the next interest calculation uses the new, larger balance. Repeat that every period and growth accelerates. A savings account, a CD and reinvested investment returns all follow this pattern, while many loans use the same math to work against you.
Simple vs compound interest
Simple interest is calculated on the original principal only, so it grows by the same dollar amount each year. Compound interest is calculated on the running balance, so each year's increase is bigger than the last.
| Year | Simple interest (5%) | Compound interest (5%, yearly) |
|---|---|---|
| Start | $10,000.00 | $10,000.00 |
| 1 | $10,500.00 | $10,500.00 |
| 5 | $12,500.00 | $12,762.82 |
| 10 | $15,000.00 | $16,288.95 |
You can compare the two side by side with the Simple Interest Calculator.
The compound interest formula
A = P(1 + r/n)^(nt)
- A
- Ending balance
- P
- Principal — the amount you start with
- r
- Annual interest rate as a decimal (5% = 0.05)
- n
- Number of compounding periods per year (12 for monthly)
- t
- Number of years
The term r/n is the rate for one period, and nt is the total number of periods. Interest earned is simply A − P.
How each input changes the result
Principal
Doubling the starting amount doubles the ending balance. Principal scales the result in a straight line.
Interest rate
The rate sits inside the exponent's base, so small differences compound into large gaps over decades. 6% for 30 years grows money about 5.7×; 8% grows it about 10×.
Compounding frequency
Monthly compounding adds interest twelve times a year instead of once. It produces a slightly higher balance than yearly compounding at the same stated rate — that is why an account's APY is a little higher than its stated rate.
Time
Time is in the exponent. Each extra year applies growth to an already-larger balance, which is why starting earlier usually matters more than any other choice.
Worked examples
Worked example
Example 1: $10,000 at 5% for 10 years, compounded monthly
- P = 10,000, r = 0.05, n = 12, t = 10
- Rate per period = 0.05 ÷ 12 ≈ 0.0041667; periods = 120
- A = 10,000 × (1.0041667)^120 ≈ 10,000 × 1.64701
Ending balance ≈ $16,470.09, of which $6,470.09 is interest.
Worked example
Example 2: monthly vs yearly compounding
- Same $10,000, 5%, 10 years, but compounded once a year
- A = 10,000 × (1.05)^10 ≈ 10,000 × 1.62889
Ending balance ≈ $16,288.95 — about $181 less than monthly compounding.
Adding regular contributions
Most people add money over time. Each deposit starts its own compounding clock, so the total is the growth of the starting balance plus the growth of every contribution. The future value of equal monthly deposits is:
FV = PMT × [(1 + i)^N − 1] ÷ i
- PMT
- Deposit each period
- i
- Rate per period (r ÷ 12)
- N
- Number of deposits
Worked example
Example 3: $200 a month at 7% for 30 years
- PMT = 200, i = 0.07 ÷ 12 ≈ 0.0058333, N = 360
- Total deposited = 200 × 360 = $72,000
Ending balance ≈ $243,994 — roughly $172,000 of it is growth, assuming a steady 7% that real investments will not deliver every year.
The Investment Calculator and Savings Calculator handle recurring deposits, and the Future Value Calculator covers single sums and annuities.
Common mistakes
- Entering 5 instead of 0.05 when using the formula by hand (calculators take the percentage directly).
- Mixing periods — using an annual rate with monthly periods without dividing by 12.
- Treating an assumed investment return as guaranteed. Market returns vary year to year.
- Ignoring fees and taxes, which reduce the rate that actually compounds.
- Forgetting inflation: a balance that doubles may buy less than double in the future.
How to use the Compound Interest Calculator
- Enter your starting principal and the annual interest rate.
- Choose how often interest compounds (monthly, yearly and so on).
- Set the number of years and any regular contribution.
- Press Calculate to see the ending balance, total interest and a year-by-year chart.
Run your own numbers
Calculate how your money can grow with compound interest.
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