You are buying a house and will borrow $330,000 on a 25-year fixed rate mortgage with monthly payments to finance the purchase. Your loan officer has offered you a mortgage with an APR of 4.15 percent. Alternatively, she tells you that you can “buy down” the interest rate to 3.8 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. How many points, at most, would you be willing to pay to buy down the interest rate? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)

The desired annual percentage rate(APR) for the borrower is 3.8% whereas the the loan officer offer is 4.15%, which means that the borrower needs to buy the interest rate from 4.15% to 3.8%

difference in interest rate=4.15%-3.8%

difference in interest rate=0.35%

We need to translate the reduction in interest rate of 0.35% to points , bearing in mind that the 1% is the same as 1 point

number of points required to buy down interest=1 point*0.35%

number of points required to buy down interest=0.350

In essence, the home loan borrower needs to buy down interest by 0.350 points in order to achieve the desired loan APR of 3.8%

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