Suppose you found a house that you want to buy, but you still have to determine

Question

Suppose you found a house that you want to buy, but you still have to determine what mortgage to use. Bank of Middle Texas has offered a 30-year fixed mortgage that requires you to pay 8% interest compounded monthly. If you take this offer, you will have to pay 3 points, which means you will have to make a payment equal to 3% of the amount borrowed at the time you sign the mortgage agreement. Bank of South Alaska has offered a 30 year fixed morgage with no points, but at an interest rate equal to 8.4% compounded monthly. For either morgage, the first payment would not be made until one month after the mortgage agreement is signed. The purchase price of the house is $250,000 and you plan to make a down payment of $40,000.

a. If you make a down payment equal to $40,000 and borrow the rest of the purchase price of the house from Bank of Middle Texas, how much will you have to pay for the 3 points when you sign the mortgage agreement?

b. Assume that the points charged by Bank of Middle Texas can simply be added to the mortgaged amount so that the total amount borrowed from the bank includes the points that must be paid at the time the mortgage is signed plus the net purchased price of the house (purchase price less the down payment). For example the points that apply to a $100,000 mortgage would be $2,000, so the morgage amount would be $102,000. Which bank offers the lower monthly payments?

c. What would the points on the Middle Texas Bank mortgage have to equal for you to be indifferent between the two mortgages?

Explanation / Answer

a)
loan amount = 210000

amount to pay for 3 points = 210000 * 3% = 6300

b)

for texas bank

total loan amount = 216300

let x be the monthly payments

=>

x * [1- (1+ 8%/12)^-360]/8%/12 = 216300

=>
x = 1587.13

for alaska bank

total loan amount = 210000

let y be monthly payments

y * [1- (1 + 8.4%/12)^-360]/8.4%/12 = 210000

=> y = 1599.86

hence texas bank offers lower monthly payment

c)

let texas bank monthly payment = 1599.86

=>

1599.86 * [1- (1+ 8%/12)^-360]/8%/12

= 218034.51

so difference = 218034.51 - 210000

= 8034.51

points = 8034.51/210000 = 3.83%

hence texas bank should offer 3.83 points

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