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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).

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b) the present value of 180 payments (the savings 40.68) at 6 % is $4820.72 so it should be done. c) At 6.56% rate, the savings will exactly offset the penalty.

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If you do the calculations you will find that the cut off point for the new loan is 6.55% (on a 15 year loan of 74,019.66+2,072.55 = 76,092.21), which gives a repayment of 664.94 (a rate of 6.56% will give you a repayment of 665.36, slightly more than your current repayment).

However, if they are no other costs, as you suggest, you must ask yourself what is in it for the mortgage company?

At 6% interest on 76,092.21 the repayment is about 642.11 giving you a monthly saving of 665.30 - 642.11 = 23.19, which means it will effectively (ignoring complicating factors such as inflation) take 7.5 years to save back the 2,072.55 that has been added to the amount you owe. So you should view this deal as a kind of lock-in, and make a decision with that in mind.

Anyway, be wary of making decisions based purely on mathematical calculations. There could be other factors to consider.

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