You are buying a house and will borrow $205,000 on a 30-year fixed rate mortgage

Question

You are buying a house and will borrow $205,000 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 4.35 percent. Alternatively, she tells you that you can “buy down” the interest rate to 4.15 percent if you pay points upfront on the loan. A point on a loan is 1 percent (one percentage point) of the loan value.

What are the most points you would 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., 32.164.)

You are buying a house and will borrow $205,000 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 4.35 percent. Alternatively, she tells you that you can “buy down” the interest rate to 4.15 percent if you pay points upfront on the loan. A point on a loan is 1 percent (one percentage point) of the loan value.

Explanation / Answer

APR = 4.35%

Monthly interest rate = 4.35%/12 = 0.3625% = 0.003625

No. of payments = 30 years * 12 = 360

Loan payment = (Loan value * Interest rate)/ {1 – (1+interest rate)-no. of payments}

Monthly loan payment of original loan = ($205,000 * 0.003625) / (1 – 1.003625-360) = $1,020.51

In case the APR is reduced to 4.15 percent, the minimum loan value shall be equal to present value of equal monthly payments.

Monthly proposed interest rate = 4.15%/12 = 0.3458% = 0.003458Loan amount = Loan payment * {1 – (1+r)-n}/r

Minimum loan amount = $1,020.51 * (1 – 1.003458-360)/0.003458 = $1,020.51 * 205.7274 = $209,484.17

Maximum upfront payment = $209,484.17 - $205,000 = $4,484.17

Maximum loan points = $4,484.17/$205,000 = 0.0218 = 2.18% = 2.18 points

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