Compound interest is the earned depending on both the initial investment and previously earned interest. To find the balance
A of an account that earns compound interest, an can be used.
In this ,
P stands for the principal, or the initial amount of money,
r is the interest rate in form, and
n is the number of times the interest is compounded per year. For an account with the principal
$100 and an annual interest of
18% compounded twice a year, the balance in the account after
t years is shown in the graph.
Notice that the function grows continuously, whereas, in reality, the account balance only increases at the times of compound. When calculating compound interest, the number of compounding periods
n creates a difference. That is, the higher the number of compounding periods, the greater the amount of compound interest.