How the Compound Interest Calculator Works
Compound interest is interest that earns interest. When you save money, the bank or the investment pays you interest. With compound interest, that interest is added to your balance, and from then on it earns interest too. Over many years, this snowball effect makes savings grow much faster than they would with plain interest. The Compound Interest Calculator shows how big it can get.
What you enter
- Starting amount: the money you have now.
- What you add: how often you add money (every month, every 3 months, every year, or never), how much, and whether it is added at the start or the end of the period. You can also raise the amount by a percentage each year.
- Interest rate: the yearly rate you expect.
- How often interest is added: yearly, twice a year, quarterly, monthly, daily, or continuously.
- Time: years and extra months.
- Inflation: used to show the result in today's money.
The formula
For a single starting amount P, a yearly rate r, interest added n times a year, and t years, the balance is:
balance = P x (1 + r / n)^(n x t)
With continuous compounding, the balance is P x e^(r x t). When you also add money regularly, the calculator grows the balance month by month, adding each contribution when it is due, and sums everything up.
A worked example: a single amount
You put $10,000 at 7% a year for 10 years. Here is the result for each way of adding the interest:
| Interest is added | Balance after 10 years |
|---|---|
| With simple interest (never added) | $17,000.00 |
| Yearly | $19,671.51 |
| Twice a year | $19,897.89 |
| Quarterly | $20,015.97 |
| Monthly | $20,096.61 |
| Daily | $20,136.18 |
| Continuously | $20,137.53 |
Simple interest gives $7,000 of interest over the ten years: $700 a year. Compounding gives nearly $10,000 or more. The more often the interest is added, the more you earn, but the gains get smaller and smaller. Going from yearly to daily adds $464.67, and going from daily to continuous adds only $1.35.
The effective yearly rate (APY)
A rate of 7% added monthly is not the same as 7% added once a year. The APY, or annual percentage yield, is the yearly rate you really get after compounding:
APY = (1 + r / n)^n - 1
For 7% added monthly, the APY is 7.229%. It is the fair way to compare savings accounts with different compounding.
A worked example: regular contributions
You start with $10,000 and add $200 at the end of every month for 20 years. The rate is 7% added monthly.
| Result | Amount |
|---|---|
| Future balance | $144,572.72 |
| Total you put in | $58,000.00 |
| Interest earned | $86,572.72 |
| With simple interest instead | $105,460.00 |
| Value in today's money at 2.5% inflation | $88,228.53 |
| Time for money to double | 9.93 years |
Chart: the balance grows faster and faster
The same example, in thousands of dollars:
Start ███ 10 Year 5 ████████ 28 Year 10 ███████████████ 55 Year 15 █████████████████████████ 92 Year 20 ████████████████████████████████████████ 145
In the first 10 years, the balance grows by about $45,000. In the last 10 years, it grows by about $90,000, twice as much, because the interest keeps earning interest.
The rule of 72
A quick way to estimate how long it takes to double your money is to divide 72 by the interest rate. At 7%, that is about 10.3 years. The calculator works out the exact figure for your rate, which is 9.93 years at an APY of 7.229%.
Tips
- Start early. Time matters more than almost anything else. The last years earn the most.
- Add regularly. Steady deposits build the balance on which the interest is earned.
- Compare the APY, not only the stated rate, when you choose an account.
- The same effect works against you with debt. Interest on a credit card is added to the balance, and then charged interest itself.
What this calculator does not include
- Taxes on the interest, and fees on the account or investment.
- A rate that changes over time. Real savings rates and investment returns move up and down.
- Withdrawals. The calculator assumes you leave the money in.
This tool gives an estimate for general information only. It is not financial or investment advice. Returns are not guaranteed.