Lesson 8. 7 More Applications for Percents

Vocabulary • • Interest Simple Interest Principal Rate

n Interest is the amount of money charged for borrowing or using money. Interest can be paid or earned. If you borrow money, you pay interest. If you deposit money into savings, you earn interest.

n n Simple Interest is a fixed percent of the principal. It is found using the formula, I = Prt, where P represents the principal, r the rate of interest, and t the time in years.

n n n Principal is the initial amount of money borrowed, saved, or invested. Rate is the percent charged on borrowing money or percent earned in saving or investing money. Time is the time in years that the money is borrowed, saved, or invested.

Example 1: Finding Interest and Total Payment on a Loan n To buy a car, Jessica borrowed $15, 000 for 3 years at an annual simple interest rate of 9%. How much interest will she pay is she pays the entire loan off at the end of the 3 rd year? What is the total amount that she will repay?

To find the amount of Interest: I=Pxrxt n I = 15, 000 x. 09 x 3 n I = $4, 050 n n To put in percent, drop the percent symbol and move the decimal 2 places to the left. (. 09) Or, drop the percent symbol and put the number over 100. (9/100)

To find the total amount: n n Once you calculate the interest, you must then add the interest to the amount that is borrowed (principal). $4, 050 + $15, 000 = $19, 050

Example 2: Determining the Amount of Investment Time n Nancy invested $6, 000 in a bond at a yearly rate of 3%. She earned $450 in interest. How long was the money invested?

I=Pxrxt n 450 = 6000 x. 03 x t n 450 = 18 x t n 450/18 = t n 2. 5 = time in years n

Example 3: Computing Total Savings n John’s parents deposited $1, 000 into a savings account as a college fund when he was born. How much will John have in this account after 18 years at a yearly simple interest rate of 3. 25%?

Use the formula: I = P x r x t n I = 1, 000 x. 0325 x 18 n I = $585 n n Then take the interest and add to the principal, the amount that was deposited. $585 + $1, 000 = $1, 585 in his savings account

Example 4: Finding the Rate of Interest n Mr. White borrowed $8, 000 for 4 years to make home improvements. If he repaid a total of $10, 320, at what interest rate did he borrow the money? n First, use the formula, P + I = A n Then, use the formula, I = P x r x t

n n n n P+I=A 8000 + I = 10320 I = $2, 320 I=Pxrxt 2320 = 8000 x r x 4 2320 = 12000 x r. 0725 = r, then multiply by 100 to change to a percentage, . 0725 x 100 = 7. 25% rate