Question

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.)

Answer 1

Approx 34 months are required to payoff the loan

Step-by-step 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