# Compound Interest Formula

## Formula

### Summary

The compound interest formula calculates the growth of a principal amount with compounding interest over time.

Expression Description
Accumulated amount.
Principal amount.
Rate of interest expressed as a decimal value.
Frequency of investment per time period.
Time elapsed.

## Usage

The compound interest formula calculates the growth of a principal amount with compounding interest over time. For example, given an interest rate of , a principal amount of , time elapsed of and a yearly investment strategy , the formula calculates the accumulated amount. This is shown below.

## Examples

### Quarterly Interest

This example calculates the accumulated value of an investment given an interest rate of , a principal amount of , time elapsed of and a quarterly investment strategy . This is shown below.

Note, while the interest rate is , the interest rate applied for each quarter is only .

### Monthly Interest

This example calculates the accumulated value of an investment given an interest rate of , a principal amount of , time elapsed of and a monthly investment strategy . This is shown below.