Compound Interest Formula Calculator

Formula

The formula to calculate compound interest is:

\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]

Where:

$ A $ is the total amount (principal + interest).
$ P $ is the principal amount.
$ r $ is the annual nominal interest rate (as a decimal).
$ n $ is the number of times interest is compounded per year.
$ t $ is the number of years.

Example

Let's say the principal ($ P $) is $1,000, the annual interest rate ($ r $) is 5%, the interest is compounded quarterly ($ n = 4 $), and the number of years ($ t $) is 10. Using the formula:

\[ A = 1000 \left(1 + \frac{0.05}{4}\right)^{4 \times 10} = 1000 \left(1 + 0.0125\right)^{40} \approx 1647.01 \]

So, the total amount after 10 years is approximately $1,647.01.

What is Compound Interest?

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It allows investments to grow faster over time compared to simple interest.