Question

Jenna's parents have given her an running shoes. interest-free loan of $100 to buy a new pair of She plans to pay back the loan with monthly $20 each a. write a function rule for the balance function B(p), where p represents the number of payments that Jenna has made. b. After how many payments will Jenna have paid back more than half the loan? Explain your reasoning. c. Suppose the loan amount were $120 and the monthly payments were $15. Write a rule for the new balance function and use it to determine how long it would take Jenna to pay off the loan.

Answer 1

A.) Since there is not interest, there is no time value of money to be recovered. That means that the $100 today, would still be $100 a few years from now. The balance function would then be:

B(p) = $100 - 20p

b.)  Since the half of 100 is 50, equate B(p) to 50

B(p) = 50 = 100 - 20p
p = 2.5

Therefore, after 3 payments, Jenna have paid back more than half of the loan.

c.1) The same procedure is done as that of part a. However, the base amount is $120 instead of $100, and the $20 is replaced with $15. The new equation becomes:

B(p) = 120 - 15p

c.2) To determine the time, let the balance zero out.

0 = 120 - 15p
Solving for p,
p = 8

Thus, Jenna could pay back the loan after 8 months.