Chapter 1.1, Problem 50E

Mortgage A couple can afford $800 per month to purchase a home. As indicated in the table, if they can get an interest rate of 7.5%, the number of years t that it will take to pay off the mortgage is a function of the dollar amount A of the mortgage for the home they purchase.

Amount A ($)	t (years)
40,000	5
69,000	10
89,000	15
103,000	20
120,000	30

(Source: Comprehensive Mortgage Tables [Publication No. 492], Financial Publishing Co.)

a.    If the couple wishes to finance $103,000, for how long must they make payments? Write this correspondence in function form if t = f(A).

b.    What is f(120,000)? Write a sentence that explains its meaning.

c.    What is f (3·40,000)?

d.    What value of A makes f(A) = 5 true?

e.    Does f (3·40,000) = 3 · f(40.000)? Explain your reasoning.