Finance formula
How to calculate compound interest
Compound interest measures growth when interest earns more interest over time.
Direct answer
Formula
A = P(1 + r / n)^(n * t)
Use the table below to match each symbol with the right input. Keep units consistent before you start.
Compound interest formula
Start here when you only need the equation and variable names.
Formula
A = P(1 + r / n)^(n * t)
Compound interest measures growth when interest earns more interest over time.
Variable meanings
Check each symbol, meaning, and unit before you calculate.
| Symbol | Name | Description | Unit |
|---|---|---|---|
| A | Final amount | Balance after compounding. | currency |
| P | Principal | Starting balance. | currency |
| r | Annual rate | Nominal annual interest rate as a decimal. | Depends on inputs |
| n | Compounding periods | Number of times interest is added each year. | Depends on inputs |
| t | Years | Length of time the money compounds. | years |
When to use this formula
Check that your situation matches the formula before you trust the result.
- Best for savings accounts, investments, and debt balances where interest is added more than once.
Step-by-step method
Follow these steps when you are solving it by hand.
- 1Convert the annual interest rate to a decimal.
- 2Divide the annual rate by the number of compounding periods per year.
- 3Raise 1 plus the period rate to the total number of periods.
- 4Multiply by the starting principal.
Examples
These sample numbers show the order of operations and units.
Monthly compounding
P
$5,000
r
0.06
n
12
t
5
- 1.A = 5000(1 + 0.06 / 12)^(12 * 5)
- 2.A = 5000(1.005)^60
- 3.A = 6744.25
Result
$5,000 grows to $6,744.25.
Quarterly compounding
P
$1,200
r
0.04
n
4
t
3
- 1.A = 1200(1 + 0.04 / 4)^(4 * 3)
- 2.A = 1200(1.01)^12
- 3.A = 1352.19
Result
$1,200 grows to $1,352.19.
Mistakes to avoid
Small input or unit errors can change the answer a lot.
- Using an annual rate where the compound interest formula needs a monthly or period rate.
- Entering 8 instead of 0.08 when the formula calls for a decimal rate.
- Comparing results across different time periods without converting them first.
- Rounding each step instead of rounding the final answer.
Open the Compound Interest Calculator
Open the calculator for the answer without rewriting the formula.
Enter your values in the related calculator, then compare the output with the hand method above.
Open Compound Interest CalculatorFAQs
Short answers for common formula questions.
Can I calculate Compound interest by hand?
Yes. Write the units next to each value, convert rates or measurements first, and round only the final answer.
Why does my Compound interest result differ from another calculator?
Most differences come from rounding, unit conversions, rate timing, or a slightly different version of the formula.
When is the Compound Interest Calculator better than hand math?
Open the Compound Interest Calculator to check several scenarios or skip the hand arithmetic.