You have an outstanding student loan with required payments of $550 per month for the next four years. The interest rate on the loan is 8% APR(compounded monthly). Now that you realize your best investment is to prepay your studentloan, you decide to prepay as much as you can each month. Looking at yourbudget, you can afford to pay an extra $175 a month in addition to your required monthly payments of $550, or $725 in total each month. How long will it take you to pay off theloan? (Note: Be careful not to round any intermediate steps less than six decimalplaces.)

There are three parts to thisproblem:

1. Compute the discount rate for the loan.

2. Compute the original loan balance.

3. Compute the time remaining until the loan is repaid with the extra payment.

First, the discount rate of the cash flow is 8%/12 = 0.6666666667 per month.

Next, compute the original outstanding balance using the followingformula:

PV = C x 1/r (1 - 1/(1+r)ⁿ

where C is the monthlypayment, r is the discountrate, and n is the number of periods.