Sign In
The interest that is applied only to an initial amount of money is called simple interest. The initial amount is known as the principal. Simple interest is calculated as a product of principal, annual interest rate, and the time in years.
An interest rate is a percent used to calculate the interest on the principal. It may be easier to write it in decimal form to make the calculations easier. For instance, assume that a savings account earns 3% simple interest per year on a deposit of $1000. 1000 * 0.03* 1= $ 30 This means that the simple interest earned on $1000 in one year is $30. The final amount of money in the account is called the balance. The following table shows the balance over five years of an account that earns 3 % simple interest each year.
Years | Amount of Simple Interest | Balance |
---|---|---|
1 | 1000 * 0.03* 1=$ 30 | 1000+30=$ 1030 |
2 | 1000 * 0.03* 2=$ 60 | 1000+60=$ 1060 |
3 | 1000 * 0.03* 3=$ 90 | 1000+90=$ 1090 |
4 | 1000 * 0.03* 4=$ 120 | 1000+120=$ 1120 |
5 | 1000 * 0.03* 5=$ 150 | 1000+150=$ 1150 |
When interest is compounded infinitely many times, it is said to be continuously compounded. Let A be the balance of an account that is continuously compounded, P the initial amount, r the interest rate, and t the time. These values are connected by the following formula.
A=Pe^(rt)
Keep in mind that, in this formula, the value of r must be written as a decimal and the time t must be in years. Also, the initial amount P is usually called principal.