Compound Interest Calculator
Grow a principal with compound interest. Enter the annual rate, the number of years, how often interest compounds, and an optional deposit for each period. 1,000 at 5% compounded yearly for 2 years grows to 1,102.50.
How to calculate compound interest
The calculator applies interest once per compounding period. It divides the annual rate by the number of periods in a year, so 5% compounded monthly uses 5% / 12 each month. A deposit is added at the end of each period and earns interest from the next period on.
future = principal × (1 + rate/n)^(n×years) + deposit × (((1 + rate/n)^(n×years) - 1) / (rate/n))
- Pick the compounding frequency n: 1 for yearly, 4 for quarterly, 12 for monthly, 365 for daily.
- Multiply the principal by (1 + rate/n) once for every period. 1,000 at 5% yearly for 2 years is 1,000 × 1.05² = 1,102.50. Interest earned is 102.50.
- Add the deposits. 1,000 at 5% compounded monthly for 1 year, plus 100 at the end of each month, grows to about 2,279.05. Of that, 1,200 is deposits and about 79.05 is interest.
At a 0% rate nothing grows, so the future value is the principal plus the deposits. A rate that makes the growth factor per period zero or negative cannot be compounded.
How compounding grows money
Compound interest pays interest on the original principal and on the interest already earned. Each period starts from a larger balance than the one before.
Simple interest pays only on the principal. 1,000 at 5% earns 50 a year, so 10 years of simple interest gives 1,500. With yearly compounding, the same 10 years gives 1,628.89.
Compare compounding frequencies
A more frequent schedule applies a smaller rate more often, and the total ends up slightly higher. The gap grows with the length of the term.
These figures start from 1,000 at a 5% annual rate with no deposits.
| Compounding | After 2 years | After 10 years | After 20 years |
|---|---|---|---|
| Yearly | 1,102.50 | 1,628.89 | 2,653.30 |
| Quarterly | 1,104.49 | 1,643.62 | 2,701.48 |
| Monthly | 1,104.94 | 1,647.01 | 2,712.64 |
| Daily | 1,105.16 | 1,648.66 | 2,718.10 |
Add regular deposits
Enter a deposit to model steady saving. The calculator adds it at the end of every compounding period, so each deposit earns interest in the periods after it.
Saving 100 a month at 5% for 1 year, starting from zero, gives about 1,227.89: 1,200 deposited and about 27.89 in interest. Over 10 years, the same plan reaches about 15,528.23, with 12,000 deposited and about 3,528.23 in interest.
- Set the compounding frequency to match your deposit schedule. Monthly deposits pair with monthly compounding.
- Leave the deposit blank to see growth on the principal alone.
- Total deposited does not include the starting principal.
Estimate doubling time
The rule of 72 gives a quick estimate. Divide 72 by the annual rate in percent to get the years needed to double. At 5%, 72 / 5 = 14.4 years.
The exact figure for yearly compounding at 5% is about 14.21 years. The rule works best for rates between about 4% and 12%.
Not the same as
Compound interest repeats a rate over time. A one-time percent does not.
- What is X percent of Y? 5% of 1,000 is 50, once. Compound interest applies the rate again to the new total. Open percent of a number
- Increase by a percent Increasing 1,000 by 5% once gives 1,050. Two years of yearly compound interest gives 1,102.50. Open increase by a percent
- Percentage change Percentage change measures growth between two values you already have. Compound interest projects a future value from a rate. Open percentage change
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Compound interest questions
1,102.50. The interest earned is 102.50.
50. That is a single percent of a number, not compound interest. The same 1,000 at 5% for 2 years becomes 1,102.50.
Each deposit is added at the end of a compounding period, so it earns interest in later periods. It earns nothing in the period you deposit it.
The rate is applied more often, so interest starts earning interest sooner. 1,000 at 5% for 2 years is 1,102.50 yearly, 1,104.49 quarterly, and 1,104.94 monthly.
The future value is the principal plus the deposits. Nothing extra is earned.
Simple interest pays only on the principal. Compound interest also pays on past interest. For 1,000 at 5% over 10 years, simple interest gives 1,500 and yearly compounding gives 1,628.89.
Enter the nominal annual rate and pick the compounding schedule. If you only have an APY, choose yearly compounding and enter the APY, because the effective yearly growth is the same.
Yes, down to a rate that keeps the growth factor per period above zero. A negative rate shrinks the balance each period.