Answer to Question #104467 in Finance for andrew

Question

You are buying a house and will borrow $225,000 on a 30-year fixed rate mortgage with monthly payments to finance the purchase. Your loan officer has offered you a mortgage with an APR of 4.3 percent. Alternatively, she tells you that you can “buy down” the interest rate to 4.05 percent if you pay points up front on the loan. A point on a loan is 1 percent (one percentage point) of the loan value. You believe that you will only live in the house for eight years before selling the house and buying another house. This means that in eight years, you will pay off the remaining balance of the original mortgage. How many points, at most, would you be willing to pay to buy down the interest rate?

Answer 1

If you repay the loan in 8 years, then the monthly payment is:

$P = 225,000*0.043/12*\frac{(1 + 0.043/12)^{8*12}}{(1 + 0.043/12)^{96} - 1} = 2,774.1$

If the APR is 4.05%, then the monthly payment should be:

$P = 225,000*0.0405/12*\frac{(1 + 0.0405/12)^{8*12}}{(1 + 0.0405/12)^{96} - 1} = 2,747.8$

1 percent point is 225,000/100 = 2,250, so there is no sence to repay $2,250 more every month, if you want to end up in 8 years.