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Chap 7 Mortgage Markets

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Item16

2points

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Item16

Item 16 2 points

Problem 7-10 (LG 7-3)

You plan to purchase a house for $160,000 using a 10-year mortgage obtained from your local bank. You will make a down payment of 15 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 6.5 percent and zero points. Option 2: Mortgage rate of 6.05 percent and 3.0 points.

b.	Your bank offers you the following two options for payment:

	Which option should you choose?
	Option 1: Mortgage rate of 7.00 percent and 1 point. Option 2: Mortgage rate of 6.75 percent and 1.5 points.

Note: There are no closing costs other than points paid.

Answer 1

One point corresponds to discount points or fees paid directly to the lender at closing in exchange for a reduced interest rate.

One point will cost 1 percent of your mortgage amount.

The initial mortgage after downpayment is 85% of the purchase price = 85% of $160,000 = $136,000; This mortgage will carry on for 10 years. Also given is that there are no prepayment of the mortgage.

To compare, we would have to check between the sum to be repaid in back.

Assuming the mortgage rate is on an annual basis, we need to find the sums of the (compounded interest+ principal) and the mortgage points.

The repayment amount can be found from the equivalent annual installment calculation multiplied with the duration of the mortgage of 10 years as there is no prior prepayment.

where N= no. of annual installments=10

R= annual rate of interest(mortgage interest)

P =mortgage amount = $136,000

We can do this and not worry about the compounding impact of the mortgage payments as EMI/EAI captures that

a)

The options are

• Option 1: Mortgage rate of 6.5 percent and zero points

  • EAI=

  • The total payment is 18918.24*10 =189182.4 as points is 0.

• Option 2: Mortgage rate of 6.05 percent and 3.0 points

• 3 points correspond to 3% of mortgage = 0.03*136000 =4080

• EAI=

• The total payment is 18521.839*10+4080 = 189298.39

I will go for Option 1, the one without mortgage points

b) The options are

• Option 1: Mortgage rate of 7.00 percent and 1 point

• 1 point corresponds to 1% of mortagage payment, i,e 1360

• .EAI =

• The total payment is 19363.34*10+1360 = 194993.4

• Option 2: Mortgage rate of 6.75 percent and 1.5 points

• 1 point corresponds to 1.5% of mortgage payment i.e 2040

• EAI=

• The total payment is 19140.179*10+ 2040 = 193441.79

• I will go for Option 1 with 1 mortgage point as the total repayment is lower.