Compound Interest Calculator
- Updated
- Formula shown
- Free, no sign-up
Results
$5,000.00 at 6% compounded monthly grows to $9,096.98 in 10 years
| Year | Interest that year | Total interest | Balance |
|---|---|---|---|
| 1 | $308.39 | $308.39 | $5,308.39 |
| 2 | $327.41 | $635.80 | $5,635.80 |
| 3 | $347.60 | $983.40 | $5,983.40 |
| 4 | $369.04 | $1,352.45 | $6,352.45 |
| 5 | $391.80 | $1,744.25 | $6,744.25 |
| 6 | $415.97 | $2,160.22 | $7,160.22 |
| 7 | $441.63 | $2,601.85 | $7,601.85 |
| 8 | $468.87 | $3,070.71 | $8,070.71 |
| 9 | $497.78 | $3,568.50 | $8,568.50 |
| 10 | $528.49 | $4,096.98 | $9,096.98 |
The rule of 72 is a rule of thumb for quick mental maths. The exact doubling time above uses ln 2 ÷ ln(1 + APY).
How to use the compound interest calculator
- Choose what to solve for: the future value, the principal you need, the rate you need, or the time it takes.
- Fill in the other three values. The rate is the nominal annual rate, as banks and loan papers usually quote it.
- Pick how often interest compounds. Choose "Continuously" for the theoretical limit used in finance and science.
- Read the answer, the effective annual rate, the doubling time and the balance at the end of each year.
Compound interest formula
Continuous: A = P × er × t
Effective annual rate = (1 + r ÷ n)n − 1
A is the future value, P the starting principal, r the annual rate as a decimal (6% = 0.06), n the number of times interest compounds each year and t the time in years. e is Euler's number, about 2.71828.
Compounding means interest is added to the balance, and the next round of interest is worked out on the bigger balance. With monthly compounding at 6%, the balance grows by 0.5% each month. Twelve of those steps make slightly more than 6% for the year, because later months earn interest on earlier interest. The effective annual rate, also called the APY or AER, measures that full-year growth so you can compare accounts that compound differently.
The formula rearranges to solve for any one value: P = A ÷ (1 + r/n)nt, t = ln(A/P) ÷ (n × ln(1 + r/n)) and r = n × ((A/P)1/(nt) − 1).
Worked example
$5,000 is invested at 6% a year, compounded monthly, for 10 years.
- Rate per month: 0.06 ÷ 12 = 0.005. Number of months: 12 × 10 = 120.
- After the first year the balance is $5,000 × 1.00512 = $5,308.39, an effective rate of 6.168%.
- After 10 years: A = $5,000 × 1.005120 = $9,096.98, so $4,096.98 is interest.
- Turning $5,000 into $10,000 at the same rate takes 11.58 years. Doing it in exactly 10 years needs 6.95% compounded monthly.
How compounding frequency changes the result
$10,000 at a nominal 6% for 10 years:
| Compounding | Effective annual rate | Balance after 10 years |
|---|---|---|
| Annually (n = 1) | 6% | $17,908.48 |
| Semi-annually (n = 2) | 6.09% | $18,061.11 |
| Quarterly (n = 4) | 6.1364% | $18,140.18 |
| Monthly (n = 12) | 6.1678% | $18,193.97 |
| Daily (n = 365) | 6.1831% | $18,220.29 |
| Continuously | 6.1837% | $18,221.19 |
More frequent compounding always helps, but the gains shrink quickly. Going from annual to monthly adds $285 here, while going from daily to continuous adds less than $1.00. The rate itself matters far more than the compounding schedule.
The rule of 72
The rule of 72 is a rule of thumb: divide 72 by the annual rate in percent to estimate how many years money takes to double. It works best between about 6% and 10%. The exact answer, with annual compounding, is ln 2 ÷ ln(1 + r).
| Annual rate | Rule of 72 estimate | Exact years (annual compounding) |
|---|---|---|
| 2% | 36 | 35 |
| 3% | 24 | 23.45 |
| 4% | 18 | 17.67 |
| 6% | 12 | 11.9 |
| 8% | 9 | 9.01 |
| 10% | 7.2 | 7.27 |
| 12% | 6 | 6.12 |
| 18% | 4 | 4.19 |
With continuous compounding the exact figure is 69.3 ÷ rate, which is why some people use a "rule of 70" for small rates.
Tips
- Compare APYs, not headline rates. 5.9% compounded daily is an APY of 6.077%, which beats 6% compounded annually.
- Time is the strongest lever. Each extra doubling period doubles the whole balance, which is why starting early matters more than small rate differences.
- The same maths works against you on debt. Unpaid card interest compounds too.
- To add regular deposits, tax or inflation, use the interest calculator. For interest that is never added to the balance, see the simple interest calculator.
Frequently asked questions
What is the compound interest formula?
A = P × (1 + r/n)^(n × t), where P is the principal, r the annual rate as a decimal, n the compounding periods per year and t the years. For example, $5,000 at 6% compounded monthly for 10 years grows to $5,000 × 1.005^120 = $9,096.98.
What is continuous compounding?
It is the limit as interest compounds more and more often, given by A = P × e^(r × t). $10,000 at 6% for 10 years grows to $18,221.19 with continuous compounding, against $18,193.97 with monthly and $17,908.48 with annual compounding.
What is the rule of 72?
A rule of thumb for doubling time: divide 72 by the annual rate in percent. At 6% it gives 72 ÷ 6 = 12 years; the exact answer with annual compounding is 11.90 years. It is most accurate for rates between about 6% and 10%.
What is the effective annual rate?
The effective annual rate (APY or AER) is the growth over a full year once compounding is included: (1 + r/n)^n − 1. A nominal 6% compounded monthly is 6.168% effective, and compounded daily it is 6.183%. Compare accounts by this figure.
What interest rate do I need to double my money in 10 years?
With monthly compounding you need about 6.95% a year, since 5,000 × (1 + 0.0695/12)^120 ≈ 10,000. With annual compounding the answer is 7.18%. Choose “Interest rate needed” in the calculator to solve for any target.