# Applications of Linear Functions

### Simple interest

With simple interest, interest is earned (charged) only on the amount lent (borrowed).

P         =                      principal
the amount lent or borrowed

i           =                     the interest rate

n          =                     the number of years

A         =                     the future value
the amount received or due at the end of n years

i(n)(P)  =                     interest on lending or borrowing

A  =  P  +  P (i) (n)

A  = P  [1+(i)(n)]        The P is factored out.

Example 1

\$12,000 is borrowed at a rate of 9 %.  How much is owed after n years?

A  = 12,000 (1+.09n)

The independent variable is n, the length of the loan.  The dependent variable is A, the amount which must be repaid.

Example 2

You borrow \$3,200 and want to pay it back in a lump sum after 4 years. How much will you have to pay if you are being charged 8% simple interest?

A  = 3,200 [1+.08(4)]

A  = 4,224

How much will you have to pay if you are being charged 10 % simple interest?

A  = 3,200 [1+.10(4)]

A  = 4,480

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