Investment
Compound interest (periodic compounding)
The general form. Divide the annual rate by compounding periods per year, add 1, raise it to the number of years times periods per year, multiply by principal. Interest earned equals A − P.
The Formula
A = P (1 + r/n)^(nt)
The general form. Divide the annual rate by compounding periods per year, add 1, raise it to the number of years times periods per year, multiply by principal. Interest earned equals A − P.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| P | Starting principal | currency | The amount deposited or invested at the start. Assumes no additional contributions. |
| r | Annual nominal interest rate as a decimal | decimal | Divide the quoted percentage by 100. An 8% rate is 0.08 in the formula, not 8. |
| n | Compounding periods per year | count/year | 1 annually, 2 semiannually, 4 quarterly, 12 monthly, 365 daily. |
| t | Time in years | years | Must be in years when r is annual. Convert months by dividing by 12. |
| A | Final amount | currency | Principal plus all accumulated interest. |
What Each Symbol Means
Pcurrency
Starting principal
The amount deposited or invested at the start. Assumes no additional contributions.
rdecimal
Annual nominal interest rate as a decimal
Divide the quoted percentage by 100. An 8% rate is 0.08 in the formula, not 8.
ncount/year
Compounding periods per year
1 annually, 2 semiannually, 4 quarterly, 12 monthly, 365 daily.
tyears
Time in years
Must be in years when r is annual. Convert months by dividing by 12.
Acurrency
Final amount
Principal plus all accumulated interest.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate compound interest page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Compound Interest, filed under Finance. Every number the guide produces comes from substituting into this one line.