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).