ou have an outstanding student loan with required payments of $ 550 per month for the next four years. The interest rate on the loan is 9 % APR (compounded monthly). Now that you realize your best investment is to prepay your student loan, you decide to prepay as much as you can each month. Looking at your budget, you can afford to pay an extra $ 250 a month in addition to your required monthly payments of $ 550 , or $ 800 in total each month. How long will it take you to pay off the loan? (Note: Be careful not to round any intermediate steps less than six decimal places.)

Approx 34 months are required to payoff the loan

Explanation:

In order to calculate How long will it take you to pay off the loan we would have to calculate first the Loan amount outstanding as follows:

Loan amount outstanding = 600 * 4 * 12 = $ 28,800

Therefore, to calculate How long will it take you to pay off the loan we use the following formula:

Amount = Payment (1 + r/n) ^t

28,800 = 775 (1+.09/12) ^t

28,800 / 775 = (1 +.0075) ^t

37.16 = (1.0075) ^ t

when we used it and trial method the compounded value comes to be 37.85 when t = 34 months

Hence, approx 34 months are required to payoff the loan