Question

You have an outstanding student loan with required payments of $600 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 student​ loan, you decide to prepay as much as you can each month. Looking at your​ budget, you can afford to pay an extra $175 a month in addition to your required monthly payments of $600​, or $775 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.) The number of months to pay off the loan is

Answer 1

Solution

Here we need to find the present value of original annuity payments that were to be given.This present value will give the principal of loan as this present value will be principal of loan

Present value of annuity=Annuity payment*((1-(1/(1+r)^n))/r)

where

n=number of periods=4*12=48

r-discount rate per period=8/12=0.666667 monthly

Annuity payment=600

Present value of annuity=600*((1-(1/(1+.00666667)^48))/.00666667)

Present value of annuity=24577.145884=Loan amount

Now since the decision has been made to give 775 as annuity payment

Loan amount=Present value of annuity=775*((1-(1/(1+.00666667)^n))/.00666667)

24577.145884=775*((1-(1/(1+.00666667)^n))/.00666667)

Solving we get n=35.746138

Thus number of months to pay will be 36 (Rounded off to 0 decimal places.You can round off the months according to requirement)

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answered by: anonymous