Question

Underwater Mortgage. Bernie Madeoff pays $250,000 for a new four-bedroom 2,400-square-foot home outside Tonophah, Nevada. He plans to make a 20% down payment, but is having trouble deciding whether he wants a 15-year fixed rate (6.397%) or 30-year fixed rate (6.878%) mortgage.

A). What is the monthly payment for both the 15- and 30-year mortgages, assuming a fully amortizing loan of equal payments for the life of the mortgage?

B) Assume that instead of making a 20% down payment, he makes a 10% down payment, and finances the remainder at 7.128% fixed interest for 15 years. What is his monthly payment?

C) Assume that the home's total value falls by 25%. If the homeowner is able to sell the house, but now at the new home value, what would be his gain or loss on the home and mortgage assuming all of the mortgage principal remains? Use the same assumptions as in part A.

Please show formulas

Answer 1

a. Computation of Monthly Paymment for both 15 and 30 Year Mortgage
15 years mortgage
Purchase Price	$2,50,000
Down Payment	$50,000
Principal	$2,00,000
Annual Rate of Interest	6.397%
monthly interest	0.533%
No. of Month ( 15X12)	180
Monthly Mortgage Payment=	$1,731
(200000*0.533%*(1+0.533%)^180)/((1+0.533%)^180-1)
30 years mortgage
Purchase Price	$2,50,000
Down Payment	$50,000
Principal	$2,00,000
Annual Rate of Interest	6.88%
monthly interest	0.57%
No. of Month ( 30X12)	360
Monthly Mortgage Payment=	$1,314
(200000*0.5731%*(1+0.5731%)^360)/((1+0.5731%)^360-1)

b.
10​% down​ payment, and finances at 7.121% fixed interest for 15 years
15 years mortgage
Purchase Price	$2,50,000
Down Payment	$50,000
Principal	$2,00,000
Annual Rate of Interest	7.13%
monthly interest	0.594%
No. of Month ( 15X12)	180
Monthly Mortgage Payment=	$1,812
(200000*0.594%*(1+0.594%)^180)/((1+0.594%)^180-1)
c.
Home Original Value
Purchase Price	$2,50,000
Fall in value by 25%	-$62,500
New Home Market value	$1,87,500
Mortgage Outstanding	$2,00,000
Gain/Loss on sale of house against mortgage alone	-$12,500