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MATH 166 Spring 2016 F.1 c Wen Liu F.1 Simple Interest and Discount Definition: Suppose a sum of money P , called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given as a decimal. Then the interest I at the end of t years is given by I = P rt The future value F at the end of t years is F = P + I = P + P rt = P (1 + rt) Definition: The present value needed to deposit into an account earning a simple annual rate of r, expressed as a decimal, in order to have a future amount F after t years is P = F 1 + rt Examples: 1. An amount of $3500 dollars is borrowed for the given length of time. (a) If t = 4 years and the annual interest rate of 9.0%, find the simple interest that is owed. (b) If t = 6 months and the annual interest rate of 9.0%, find the amount due at the end of the given length of time. (c) If the amount due at the end of 9 months is $3700, find the annual simple interest rate. 2. Find the present amount needed to attain a future amount of $7700 dollars in 2 years using an annual simple interest rate of 8.2%. Page 1 of 2 MATH 166 Spring 2016 F.1 c Wen Liu 3. A principal of $5000 earns 9% per year simple interest. How long will it take for the future value to become $5855? Page 2 of 2