There's a $30$-year home loan for \$$100000$ at $7$%. After $15$ years the loan is paid off in order to refinance at a lower rate. The loan has a prepayment penalty of six months interest of $80$% of the remaining balance of the loan.
a) How much is the remaining balance of the loan?
b) If the loan can be refinanced with a $15$ year loan at $6$% with no other costs, then should it be done?
c) If the loan can be refinanced over $15$ years with no other costs, then what interest rate would make it worthwhile?
I believe I got (a)
\begin{array}{|c|c|c|c|c|} \hline \text{month} &\text{payment}&\text{interest}&\text{principal}&\text{remaining}\ \\ \hline 180 &665.30&433.14&232.16&74019.66\\\hline \end{array}
Not sure about b or c though.
I attempted b by taking $74019.66$ and making that my new loan. Find a new payment across $15$ years at $6$%, which is $624.62$. I figured $665.30-624.62 = 40.68$ in savings per month.
One thing I don't know is does prepayment go into the new loan or do you pay out of pocket. If you pay out of pocket then you would save $\$7322.4 – \$2072.55$ (prepayment penalty).
Best Answer
I think they want you to increase the balance by the prepayment penalty (so there is no out of pocket cost), then see if the payment is higher or lower. So for (b) you figure the new payment on $74019.66+2072.55$ and see if it is lower. For (c) you find the interest rate on the same balance that keeps the payment the same as today.
I'm not sure I agree with this criterion for a decision in the real world-there is too much chance you will end up paying the loan off early so having the balance higher is a negative. But I think it is the way you understand the technique in the absence of other instructions. It might help to clearly lay out your assumptions.