The Compound Interest Formula

Formula

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

Used to calculate: The future value of a principal amount when interest is compounded at regular intervals.

—

What Is the Compound Interest Formula?

The compound interest formula calculates the future value of an initial principal when interest is periodically added to the balance. Unlike simple interest, compound interest allows previously accumulated interest to earn additional interest during subsequent compounding periods.

—

Formula and Variables

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

—

How to Use the Formula

Identify the principal, annual interest rate, number of compounding periods per year, and time in years. Convert the annual interest rate from a percentage to a decimal if necessary. Divide the annual rate by the number of compounding periods per year, then raise the resulting growth factor to the total number of compounding periods, nt. Multiply by the principal to find the accumulated amount.

—

When Is This Formula Used?

The compound interest formula is used when interest is periodically added to a balance and subsequent interest is calculated on both the original principal and previously accumulated interest.

Common uses:

– Calculating the future value of savings or investments
– Calculating balances on financial accounts that compound interest
– Comparing financial arrangements with different compounding frequencies

—

Important Notes

– More frequent compounding generally produces a larger accumulated amount when the principal, positive nominal annual rate, and time are otherwise the same.
– The standard formula assumes a constant nominal annual interest rate and regular compounding frequency over the specified time.
– n must be a positive number of compounding periods per year, and t is expressed in years when r is an annual rate.
– A common point of confusion is using r as a percentage instead of a decimal. For example, 5% is entered as 0.05.

—

Alternate Forms

Alternate form:

I = A - P

Alternate form:

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

Alternate form:

A = Pe^{rt}

—

Related Formulas

• The Simple Interest Formula
• The Percent Change Formula
• The Percentage Formula