- #1
issacnewton
- 1,002
- 31
Homework Statement
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 9% APR (monthly). You are
considering making an extra payment of $100 today (i.e., you will pay an extra $100
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 effective rate of return (expressed as an APR with monthly
compounding) have you earned on the $100?
Homework Equations
Annuity Formula
The Attempt at a Solution
I will present my solution for the first part. I have question about the second part. Since APR is 9%, the periodic monthly interest rate is ##i = 0.09/12 = 0.0075##. Let ##C= $500## be the monthly payment. There are 48 months in 4 years. So we can find the loan value using PV of annuity formula $$\text{PV} = \frac{500}{0.0075}\left[ 1 - \frac{1}{\left(1+ 0.0075\right)^{48}}\right] $$ Now student makes an extra payment of $100 today and then 47 payments of $500 and one last payment. Let's call this last payment ##x##. The present value of all these payments must equal to ##\text{PV}##. So, we have $$\text{PV} = 100+\frac{500}{0.0075}\left[ 1 - \frac{1}{\left(1+ 0.0075\right)^{47}}\right] + \frac{x}{\left(1+0.0075\right)^{48}} $$ Solving for ##x##, I get the last payment as ##x=$356.86##. Is this correct so far ? Now I don't the last part of the question. How would I get the effective rate of return earned on $100. What exactly is being asked here ?
Thanks