Question

4. You want to buy a house valued at $1.2 million. For a house this valuable, the lenders demand a down payment of 25% and insist that the monthly payment on the 25 year mortgage loan is no more than 30% of your monthly gross income. The quoted rate on a 25 year fixed rate mortgage loan is 2.94% per year. Assume that you can make the down payment.

(a): What is the least amount of your yearly gross income for you to qualify for the loan?

(b): Suppose you qualify for the loan, buy the house on September 1, 2020, and make the first monthly payment on October 1, 2020. What percentage of the house do you own at the end of year 2025 assuming that there has been no change in the value of the house?

Answer 1

(a)

Value of the house = 1.2 million

= $1,200,000

Down payment made = 25% of $1,200,000

= $300,000

Balance amount =$1,200,000-$300,00

= $900,000

Time =25years

Rate of interest = 2.94 % per year

Payment made every month

Total number of instalments = 25*12

= 300

Let principal part of each month will be equal

Hence, principal part of each month =Total amount due / number of instalments

= $900,000 / 300

=$3,000

Interest for first month i.e. for the month of September= 900,000*2.94/100*1/12

= $2,205

Value of first monthly instalment i.e. payment made on 1st October = $3,000+$2,205

= $5,205

Here, lender insist that the monthly payment on the 25 year mortgage loan is no more than 30% of monthly gross income .

Monthly payment including principal part and interest part too.

Hence,

Required monthly gross income = $5,205 / 30 *100

=$ 17,350

Least amount of yearly gross income to qualify for the loan = $17,350*12

=$208,200

(b) Number of instalment paid at the end of year 2025 i.e. December 2025 :

Number of instalments paid in 2020= 3

Number of instalments paid in 2021 = 12

Number of instalments paid in 2022= 12

Number of instalments paid in 2023 = 12

Number of instalments paid in 2024 = 12

Number of instalments paid in 2025 = 12

Total number of instalments = 63

​​​​​​Total amount paid during these year (Principal) + Down payment

= $3,000*63 = $189,000

Percentage of house own at the end of year 2025 = ( $189,000 + $300,000) / 1,200,000*100

= 40.75%

THANK YOU !

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