6.7 Simple Interest

Definitions:

 Interest (I): Money paid for the use of money  Principal (P): Amount of money you deposit or borrow   Interest Rate (r): The percent of increase in the principal Time (t): # of years the money is in the “bank”  Simple Interest: When interest is only paid on the principal.

Formulas:

Finding the simple interest:  Interest = Principal x Rate x Time (in years) Short-cut: I = Prt Finding the BALANCE or Principal in the account:  Balance = Principal + Prt Short-cut: A = P + Prt “A” stands for Balance

Example #1:

 Nick borrowed $7150, to be repaid after 5 years at an annual simple interest rate of 6.25%. How much interest will be due after 5 years? How much will Nick have to repay?

I = P r t I = 7150 • 6.25% • 5 A = P + Prt A = 7150 + 2234.38

I = 7150 • 0.0625 • 5 I = 2234.375

I = $2234.38

A = $9384.38

The interest was $2234.38 and he had to repay $9384.38

Ex. #2: Mr. Wong invested $4000 in a bond with a yearly interest rate of 4%. His total interest on the investment was $800. What was the length of the investment?

 I = P r t 800 = 4000 • 4% • t 800 = 4000 • 0.04 • t 800 = 160 t 160 160 5 = t The length of the investment was 5 years.

Ex. #3: Tom borrowed $35,000 to remodel his house. At the end of the 5 year loan, he had repaid a total of $46,375. At what simple interest rate did he borrow the money?

 A = P + P r t 46375 = 35000 + 35000 • r • 5 46375 = 35000 + 175000 r -35000 -35000 11375 = 175000r 175000 175000 0.065 = r The simple interest rate was 6.5%

Note: Time is in YEARS!!

 3 3 months = 12  1 year 4  6 months = 6 12  1 year 2  7 months = 7 12 year