# Document 10435122 ```MATH 166 Spring 2016
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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%.
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MATH 166 Spring 2016
F.1
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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?
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