Compound Interest
Compound Interest
\[A = P\left(1+\frac{r}{n}\right)^{nt}\]
Variables
A = compound amount
P = principal amount
r = annual interest rate
n = number of compounding periods per year
t = time period
Description
What is this formula?
The compound interest formula calculates the future value of an investment or loan where interest is periodically added to the principal.
When to use it
Use this formula when interest is compounded at regular intervals such as annually, monthly, or daily.
Example
If 1000 USD is invested at an annual interest rate of 5% compounded monthly for 3 years:
A = 1000(1 + 0.05/12)^(12×3) ≈ 1161.47 USD
Applications
Savings accounts, investment growth analysis, loans, mortgages, and financial planning.
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