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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 = Prt A = P + Prt I = 7150 • 6.25% • 5 A = 7150 + 2234.38 I = 7150 • 0.0625 • 5 A = $9384.38 I = 2234.375 I = $2234.38 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 = Prt 800 = 4000 • 4% • t 800 = 4000 • 0.04 • t 800 = 160t 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 + Prt 46375 = 35000 + 35000 • r • 5 46375 = 35000 + 175000r -35000 -35000 11375 = 175000r 175000 175000 0.065 = r The simple interest rate was 6.5% Note: Time is in YEARS!! 3 1 3 months = year 12 4 6 months = 7 year 7 months = 12 6 1 year 12 2