Calculator 02 · Growth
Simple vs compound interest
Same money, same rate, two rules. Simple interest is paid on the starting amount only; compound interest is paid on the interest as well. Watch the gap open up.
Your figuresp. 1
The two balancesp. 2
Simple · 20 yrs$20,000
Compound · Monthly$27,126
Interest on interest adds $7,126.40: compound interest earns $17,126.40 against $10,000.00 for simple interest. The compound balance passes double the starting amount in year 14.
- Compound
- Simple
Year-by-year table
| Line | Year | Simple | Compound | Difference |
|---|---|---|---|---|
| 01 | 1 | $10,500.00 | $10,511.62 | $11.62 |
| 02 | 2 | $11,000.00 | $11,049.41 | $49.41 |
| 03 | 3 | $11,500.00 | $11,614.72 | $114.72 |
| 04 | 4 | $12,000.00 | $12,208.95 | $208.95 |
| 05 | 5 | $12,500.00 | $12,833.59 | $333.59 |
| 06 | 6 | $13,000.00 | $13,490.18 | $490.18 |
| 07 | 7 | $13,500.00 | $14,180.36 | $680.36 |
| 08 | 8 | $14,000.00 | $14,905.85 | $905.85 |
| 09 | 9 | $14,500.00 | $15,668.47 | $1,168.47 |
| 10 | 10 | $15,000.00 | $16,470.09 | $1,470.09 |
| 11 | 11 | $15,500.00 | $17,312.74 | $1,812.74 |
| 12 | 12 | $16,000.00 | $18,198.49 | $2,198.49 |
| 13 | 13 | $16,500.00 | $19,129.56 | $2,629.56 |
| 14 | 14 | $17,000.00 | $20,108.26 | $3,108.26 |
| 15 | 15 | $17,500.00 | $21,137.04 | $3,637.04 |
| 16 | 16 | $18,000.00 | $22,218.45 | $4,218.45 |
| 17 | 17 | $18,500.00 | $23,355.19 | $4,855.19 |
| 18 | 18 | $19,000.00 | $24,550.08 | $5,550.08 |
| 19 | 19 | $19,500.00 | $25,806.11 | $6,306.11 |
| 20 | 20 | $20,000.00 | $27,126.40 | $7,126.40 |
Educational use only — not financial advice. The rate is an example you choose, not a forecast of what any account or investment will pay.
How the two rules work
Simple interest pays the same amount every year: principal × rate. $10,000 at 5% earns $500 a year, so after 20 years the balance is $20,000.
simple: A = P × (1 + r × t)
compound: A = P × (1 + r ÷ n)n × t
Compound interest adds each period's interest to the balance, so the next period's interest is a little larger. The same $10,000 at 5% compounded monthly (n = 12) reaches $27,126.40 after 20 years: $7,126.40 more than simple interest, all of it interest earned on interest.
The effect works just as hard against you on debt. A card balance you do not pay down compounds too, which is why unpaid interest grows faster than the rate alone suggests.
To use the calculator, enter an amount, a yearly rate and a number of years. Hover over the chart, or focus it and use the arrow keys, to read any year; the table under it lists every year and downloads as a CSV file.
Sources
- U.S. Securities and Exchange Commission, Investor.gov, Compound interest calculator: the compound growth formula with a chosen compounding frequency.
- Consumer Financial Protection Bureau, Regulation DD, Appendix A to Part 1030: how compounding is reflected in an account's annual percentage yield.
Questions
Where is simple interest still used?
Many car loans are "simple interest" loans: interest is worked out on the balance but never added to it, so you do not pay interest on interest as long as you pay on time. Bonds and accounts that pay their interest out to you behave the same way unless you reinvest it.
Why are the two equal after one year?
With annual compounding no interest has been added yet in the first year, so both rules give P × (1 + r). From year two the compound balance includes last year's interest. With monthly or daily compounding the gap starts within the first year.
How long until the money doubles?
The result marks the first whole year the compound balance is at least twice the start. The rule of 72 is a quick check: 72 ÷ 5 = 14.4 years at 5%. Under simple interest, doubling takes 1 ÷ rate, which is 20 years at 5%.