# mortgage math problem

There's a 30yr home loan for \$100,000 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 15yr loan at 6% with no other costs, then should it be done? c) If the loan can be refinanced over 15 yrs with no other costs, then what interest rate would make it worthwhile?

I believe i got (a)

```month payment interest principal remaining 180 | 665.30 | 433.14 | 232.16 | 74019.66```

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 @ 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).