Question

You have an outstanding student loan with required payments of $500 per month for the next four years. The interest rate on the loan is 8% APR. You are considering making an extra payment of $200 today (that is, you will pay an extra $200 that you are not required to pay).

If you are required to continue to make payments of $500 per month until the loan is paid off, what is the amount of your final payment?

What rate of return (expressed as an APR with monthly compounding) have you earned on the $200?

Answer 1

Monthly payments required to pay off the student debt = $ 500

No of Months to be paid = 48

APR = 8%.

Amount of Student loan can be calculated in excel by PV formula, PV(8%/12,48,500) = $ 20480.96.

If we make a $ 200 payment now, loan amount will be reduced to 20480.96 - 200 = $ 20280.96.

And if we keep paying $ 500 PM, loan amount we would ve repaid in 47 mnths = PV(8%/12,47,500) = $ 20117.50.

Outstanding loan amount at the end of 47mnths will be 20280.96 -20117.50  

= 163.46

Our final Installment will be $ 163.46 + one month interest on 163.46 = 163.46 + (163.46* 8%/12) = 163.46+1.09 =$ 164.55

$ 200 payment now have resulted in (500-164.55) = $ 335.45 less payment in 48mnths time.

Interest Earned = 335.45 -200 = 135.45,

Rate of return compounded monthly = as the payment is made against a loan which is charging 8%, it is safe to assume, we have earned 8%