You plan to purchase a house for $300,000 using a 25-year mortgage obtained from

Question

You plan to purchase a house for $300,000 using a 25-year mortgage obtained from your local bank. You will make a down payment of 10 percent of the purchase price. You will not pay off the mortgage early. Assume the homeowner will remain in the house for the full term and ignore taxes in your analysis.

a. Your bank offers you the following two options for payment: Which option should you choose? Option 1: Mortgage rate of 6.60 percent and zero points. Option 2: Mortgage rate of 6.20 percent and 1.5 points.

b. Your bank offers you the following two options for payments: Which option should you choose? Option 1: Mortgage rate of 6.20 percent and 0.5 point. Option 2: Mortgage rate of 6.10 percent and 1.0 points. Note: There are no closing costs other than points paid.

Explanation / Answer

loan amount = 300000 * 0.9 = 270000

a)

present value of annuity = payment per period * [ 1 - (1+i)^-n ]/i

option1:

270000 = PMT *[1-(1+6.6%/12)^-300]/6.6%/12

=>

PMT = 1839.97

option 2:

270000 = PMT *[1-(1+6.2%/12)^-300]/6.2%/12

PMT = 1772.77

savings in choosing option 2 = 1839.97 - 1772.77 = 67.2

present value of savings = 67.2 * [1-(1+6.2%/12)^-300]/6.2%/12

= 10234.82

initial pay in points = 300000 * 1.5% = 4500

hence choose option 2 , because the savings are higher than the cost associated

b)

present value of annuity = payment per period * [ 1 - (1+i)^-n ]/i

option1:

270000 = PMT *[1-(1+6.2%/12)^-300]/6.2%/12

=>

PMT = 1772.77

option 2:

270000 = PMT *[1-(1+6.1%/12)^-300]/6.1%/12

PMT = 1756.16

savings in choosing option 2 = 1772.77- 1756.16 = 16.61

present value of savings = 16.61 * [1-(1+6.1%/12)^-300]/6.1%/12

= 2553.70

initial pay in points for option 1 = 300000 * 0.5% = 1500

intial pay in points for option 2 = 300000 * 1% = 3000

difference = 3000 - 1500 + 2553.70 = 4053.7

hence choose option 2 because it will result positive savings

hence choose option 2 , because the savings are higher than the cost associated

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