Question

You are purchasing a new home and need to borrow $325,000 from a mortgage lender. The lender quotes a rate of 6.5% APR for a 30-year fixed rate mortgage (with payments made at the end of each month). The lender offers you the option to "buy down" the interest rate. If you pay 1 point, the interest rate will be reduced to 6.25% APR for a 30year fixed rate mortgage. One point is equal to 1% of the loan value. So if you pay the point, you will effectively pay 1% of the stated loan amount in order to reduce your monthly payments. Monthly payments are calculated based on the stated loan amount, which in this case is $325,000. Assuming you do not intend to prepay your mortgage (i.e., pay off your mortgage early), what is the effective annual rate of return of paying the point? Hint: think in terms of incremental costs and benefits.

Answer 1

Loan amount = 325,000

1% of loan amount = 1%*325,000 = 3,250

Effective loan amount = 325,000 + 3,250 = 328,250

Monthly payment amount: PV = 328,250; n = 30*12 = 360; rate = 6.25%/12 = 0.521%; CPT PMT.

PMT = 2,021.09

To find the monthly effective rate of return:

PV = 325,000; PMT = 2,021.09; N = 360, CPT rate. rate = 0.529%

Effective annual rate = (1+0.529%)^12 -1 = 6.53%

Annual percentage rate = 0.529%*12 = 6.34%