Simple vs Compound Interest
Two ways of charging or earning interest can give very different totals over time. This guide shows the arithmetic behind each, with tables you can check using the calculators.
Simple interest: a straight line
I = P × r × t
- P
- principal (starting amount)
- r
- annual rate as a decimal
- t
- time in years
Interest is calculated only on the original principal, so the same amount is added every year. 1,000 at 5% earns 50 a year, every year.
Compound interest: interest on interest
A = P × (1 + r/n)^(n × t)
- n
- number of times interest is added per year
Each time interest is added, it becomes part of the balance and earns interest itself. The growth is slow at first and speeds up over time.
Side by side
| Years | Simple interest | Compounded annually | Compounded monthly |
|---|---|---|---|
| 1 | 1,050.00 | 1,050.00 | 1,051.16 |
| 5 | 1,250.00 | 1,276.28 | 1,283.36 |
| 10 | 1,500.00 | 1,628.89 | 1,647.01 |
| 20 | 2,000.00 | 2,653.30 | 2,712.64 |
| 30 | 2,500.00 | 4,321.94 | 4,467.74 |
After one year the simple and annually compounded balances are identical; after 30 years the compounded balance is more than 70% higher than the simple one.
Does compounding frequency matter?
More frequent compounding adds a little more, but the effect shrinks quickly. The figure that captures it is the effective annual rate (also called APY or EAR): a 5% nominal rate compounded monthly is effectively 5.1162% a year, and compounded continuously it is 5.1271%. When comparing two rates with different compounding, compare their effective annual rates — the APR to APY calculator does this.
The rule of 72
A quick way to estimate how long a balance takes to double with annual compounding: divide 72 by the rate in percent. The exact doubling time is ln 2 ÷ ln(1 + r).
| Rate | Rule of 72 estimate (years) | Exact (years) |
|---|---|---|
| 2% | 36 | 35 |
| 4% | 18 | 17.7 |
| 6% | 12 | 11.9 |
| 8% | 9 | 9 |
| 10% | 7.2 | 7.3 |
| 12% | 6 | 6.1 |
Where each one is used
- Simple interest appears in some short-term loans and in interest charged for a set number of days, such as late-payment interest.
- Compound interest applies to most savings accounts, many loans and any balance where interest is left to accumulate.
- Loan repayments are a special case: interest is charged on the remaining balance each month and the payment covers it, so it does not build up — while the rest of the payment reduces the balance. See how loan amortization works.