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