Compound Interest Calculator
- Free
- No sign-up
- Works on phones
- Shows the working
By Yasir Hafeez · Updated
This compound interest calculator shows how money grows when interest earns interest. Enter the principal, the annual interest rate, how often interest is compounded (yearly, half-yearly, quarterly, monthly, daily or continuously) and the number of years. It returns the final balance, the interest earned, the effective annual rate, the simple-interest amount for comparison, and a year-by-year balance table.
It’s free and needs no sign-up. It’s for learning and estimates; it doesn’t include fees, taxes or regular deposits.
How to use it
- Enter the principal P, the starting amount.
- Enter the annual rate in percent (5 for 5%).
- Choose how often interest is compounded.
- Enter the number of years and press Calculate.
Formula
$$A = P\left(1 + \frac{r}{n}\right)^{nt}$$
where r is the annual rate as a decimal, n the number of compounding periods per year and t the time in years. With continuous compounding, \( A = Pe^{rt} \). The interest earned is \( A - P \).
Worked example
\$1000 at 5% compounded monthly for 10 years (as loaded above):
$$A = 1000\left(1 + \frac{0.05}{12}\right)^{120} \approx \$1647.01$$
The interest earned is \$647.01. Simple interest would give only \$1500, so compounding adds \$147.01. Compounded continuously, the balance would be \( 1000e^{0.5} \approx \$1648.72 \).
Worked example: quarterly
\$5000 at 6% compounded quarterly for 8 years: \( A = 5000(1.015)^{32} \approx \$8051.62 \).
How compounding frequency matters
For \$1000 at 5% for 10 years:
| Compounded | Final amount |
|---|---|
| Yearly | \$1628.89 |
| Monthly | \$1647.01 |
| Daily | \$1648.66 |
| Continuously | \$1648.72 |
More frequent compounding helps, but with rapidly diminishing returns, approaching the continuous limit \( Pe^{rt} \). That limit is where the number \( e \) comes from; see exponential functions.
The rule of 72
Money doubles in roughly \( 72 \div \text{rate} \) years: at 6%, about 12 years. The exact doubling time for yearly compounding is \( \frac{\ln 2}{\ln(1 + r)} \), found with logarithms.
Common mistakes
- Using the rate as a whole number. 5% is 0.05 in the formula (the calculator takes 5 and converts it).
- Mixing up n and t. n is periods per year, t is years; the exponent is \( nt \).
- Comparing nominal rates with different compounding. Compare effective annual rates instead.
Related guides
Further reading
- Compound interest (Wikipedia) — the formula, continuous compounding and history.
FAQ
What is the compound interest formula?
\( A = P\left(1 + \frac{r}{n}\right)^{nt} \).
What is the difference between simple and compound interest?
Simple interest is paid only on the original amount; compound interest is also paid on earlier interest, so the balance grows faster.
How much is \$1000 at 5% for 10 years?
About \$1628.89 compounded yearly, or \$1647.01 compounded monthly.
What is continuous compounding?
The limit of compounding more and more often: \( A = Pe^{rt} \).