33) Tony is offering two repayment plans to Phil for a long overdue loan. Offer 1 is to receive a visit from an enforcer and the debt is due in full at once. Offer 2 is to pay back $3,900 per year at a 20% interest rate until Phil pays off the loan principal. Phil owes Tony $15,000. How long will it take Phil to pay off the loan if he takes offer 2?

The answer is 8 years.

Explanation:

In Offer 2, we apply the present value formular for annuity to calculate the number of repayment, thus number of year payback because repayment is made once a year.

We have the formular to calculate present value of annuity as followed:

PV = (C/i) x [1 - (1+i) ^ (-n) ].

apply to the question, we have:

PV = the owed principal amount = $15,000;

i = annual interest rate compounded once a year = 20%;

C = number of equal annual repayment = $3,900;

n: number of repayment made thus number of year payback.

As we need to find n, we have:

15,000 = (3,900/20%) x [ 1 - 1.20^ (-n) ] 1-1.2^ (-n) = 0.769 1.2 (^-n) = 0.231 n = - (the base 1.2 logarithm of 0.231) = 8