Year by year
$10,000.00 at 5% a year, with interest added monthly.
| Year | Interest that year | Balance |
|---|---|---|
| 1 | $511.62 | $10,511.62 |
| 2 | $537.79 | $11,049.41 |
| 3 | $565.31 | $11,614.72 |
| 4 | $594.23 | $12,208.95 |
| 5 | $624.63 | $12,833.59 |
| 6 | $656.59 | $13,490.18 |
| 7 | $690.18 | $14,180.36 |
| 8 | $725.49 | $14,905.85 |
| 9 | $762.61 | $15,668.47 |
| 10 | $801.63 | $16,470.09 |
The interest column grows every year even though the rate stays the same. That widening gap is the whole point of compounding. Periods longer than 30 years show every fifth year.
Results are estimates for planning. They are not financial, tax or legal advice.
The compound interest formula
- A is the balance at the end.
- P is the starting amount, also called the principal.
- r is the yearly interest rate as a decimal, so 5% is 0.05.
- n is how many times a year interest is added: 12 for monthly, 365 for daily.
- t is the time in years.
The interest earned is A − P. When interest is added continuously, the formula becomes A = P × e^(r × t), where e is about 2.71828.
Worked examples
$10,000 at 5% for 10 years, compounded monthly
The rate for one month is 0.05 ÷ 12 = 0.0041667, and there are 12 × 10 = 120 months. Raising 1.0041667 to the power 120 gives a growth factor of 1.647009, so the balance is 10,000 × 1.647009 = $16,470.09. Of that, $6,470.09 is interest.
A savings certificate that pays quarterly
$2,500 at 4.5% compounded quarterly for 3 years: the quarterly rate is 0.045 ÷ 4 = 0.01125 and there are 12 quarters. 2,500 × 1.01125^12 = $2,859.19, which is $359.19 of interest. Simple interest on the same deposit would pay 2,500 × 0.045 × 3 = $337.50, so compounding added $21.69.
The same money, compounded five ways
$10,000 at 5% for 10 years, changing only how often interest is added:
| Interest is added | After 10 years | APY |
|---|---|---|
| Yearly | $16,288.95 | 5.000% |
| Twice a year | $16,386.16 | 5.063% |
| Quarterly | $16,436.19 | 5.095% |
| Monthly | $16,470.09 | 5.116% |
| Daily | $16,486.65 | 5.127% |
| Continuously | $16,487.21 | 5.127% |
Going from yearly to monthly adds $181. Going from monthly to continuous adds only $17. There is a ceiling on what more frequent compounding can do.
Interest rate, APR and APY
The rate you type in is the yearly rate before compounding. The APY (annual percentage yield) is what that rate comes to over a full year once compounding is counted:
In the United States, banks and credit unions have to state the APY on savings accounts and certificates, worked out in a standard way, so that accounts can be compared like for like. The rule is the Truth in Savings Act, put into practice by Regulation DD (12 CFR Part 1030). Two accounts with the same APY pay the same over a year, however often each one compounds.
How long until money doubles: the rule of 72
Divide 72 by the yearly rate to estimate the years needed to double. It is a rule of thumb that works well for everyday rates:
| Yearly rate | Rule of 72 | Exact |
|---|---|---|
| 2% | 36 years | 35.0 years |
| 4% | 18 years | 17.7 years |
| 6% | 12 years | 11.9 years |
| 8% | 9 years | 9.0 years |
| 12% | 6 years | 6.1 years |
The exact figure is ln(2) ÷ ln(1 + r) for yearly compounding. Time does more than rate over long stretches: $5,000 left for 30 years becomes $16,216.99 at 4% and $50,313.28 at 8%. Doubling the rate more than tripled the result.
Adding money as you go
This calculator follows one sum that is left alone. If you add to it every month, or take money out, use the investment calculator, which handles regular deposits and withdrawals.
Questions people ask
What is compound interest?
It is interest paid on your interest as well as on the money you put in. Each time interest is added, the balance gets bigger, so the next round of interest is worked out on a larger amount.
How is compound interest different from simple interest?
Simple interest is paid only on the original amount. $1,000 at 5% simple interest earns $50 every year, so $100 after two years. Compounded yearly, the second year pays 5% of $1,050, which is $52.50, so you have $1,102.50.
Does daily compounding beat monthly by much?
Not by much. $10,000 at 5% for 10 years reaches $16,470.09 compounded monthly and $16,486.65 compounded daily, a gap of $16.56. The rate and the length of time matter far more than how often interest is added.
What is the difference between an interest rate and APY?
The interest rate (or APR) is the yearly rate before compounding. APY is what you really earn over a year once compounding is included. A 5% rate compounded monthly is an APY of 5.116%. If a bank quotes you an APY, choose “Yearly” here and enter the APY as the rate.
How long does it take money to double?
Divide 72 by the yearly rate for a quick estimate: at 6% that is 72 ÷ 6 = 12 years. The exact answer for 6% compounded yearly is 11.9 years. The calculator shows the exact doubling time under the working.
Can I use this for debt?
Yes, for a balance that nobody is paying down. $3,000 on a card at 24% compounded daily grows to $3,813.45 in a year. A loan with regular payments needs a loan calculator, because each payment changes the balance that interest is charged on.