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.
