Imagine you put in a savings account with a yearly interest rate of .
After one year, you have . After two years, if the interest is simple , you will have (adding of the original principal amount each year.) But if it is compound interest , then in the second year you will earn of the new amount:
Yearly Compound Interest Formula
If you put dollars in a savings account with an annual interest rate , and the interest is compounded yearly, then the amount you have after years is given by the formula:
Suppose you invest at interest, compounded yearly. Find the amount you have after years.
Here, , , and . Substituting the values in the formula, we get:
Therefore, the amount after years would be about .
General Compound Interest Formula
If interest is compounded more frequently than once a year, you get an even better deal. In this case you have to divide the interest rate by the number of periods of compounding.
If you invest dollars at an annual interest rate , compounded times a year, then the amount you have after years is given by the formula:
Suppose you invest at interest, compounded monthly. Find the amount you have after months.
Here , , , and (since months = one and a half years).
Substituting the values, we get:
Rounding to the nearest cent, you have .