Compound Interest Formula and Calculation

Study Notes

Compound Interest Formula

Compound interest involves earning interest not only on the initial investment but also on all previous amounts of interest earned. This means that interest is added to the principal amount, which now includes both the initial investment and interest from prior periods. This concept can be illustrated with the following general formula for calculating compound interest:

[ A = P(1 + r)^t ]

where (A) represents the future value of the original investment after (t) number of years, (P) represents the initial principal amount invested, (r) is the annual rate of return expressed as a decimal, and (t) is the total number of time intervals over which interest is compounded.

Therefore, if you want to know how much money your investment will grow to when compound interest is applied to it, you would plug in these values into the formula. Below is an example using this formula:

Example: Let's say you have $1000 sitting in a savings account that earns 7% interest per year. If you leave this money untouched for 30 years, what will be the future value of your investment?

To solve this problem, we first need to determine the future value. We'll do this by calculating the compound interest:

[ FV = P \times (1 + r)^t ] [ FV = 1000 \times (1 + .07)^30 ] [ FV = 1000 \times 2.9896 ] [ FV = 2989.60 ]

So, after 30 years at a 7% annual interest rate, you would have approximately $2989.60 in your account.

This formula allows us to calculate the future value of an investment based on its initial value ((P)), annual rate of return ((r)), and time period ((t)) during which interest is compounded.

Description

Learn how to calculate compound interest using the formula A = P(1 + r)^t. Understand the concept of earning interest on both the initial investment and previous interest amounts. Explore an example calculation to determine the future value of an investment over time.