Suppose you take out a 20-year mortgage for a house that costs $397744. Assume t
ID: 3148921 • Letter: S
Question
Suppose you take out a 20-year mortgage for a house that costs $397744. Assume the following:
The annual interest rate on the mortgage is 5%.
The bank requires a minimum down payment of 17% at the time of the loan.
The annual property tax is 2.4% of the cost of the house.
The annual homeowner's insurance is 1.3% of the cost of the house.
The monthly PMI is $68
Your other long-term debts require payments of $558 per month.
If you make the minimum down payment, what is the minimum gross monthly salary you must earn in order to satisfy the 28% rule and the 36% rule simultaneously?
Explanation / Answer
TOTAL LOAN AMOUNT FOR HOUSE AFTER PAYING DOWN PAYMENT= 397744 X 83% = 330,128 (AS MINIMUM DOWN PAYMENT 17%)
FOR REPAYMENT OF THIS LOAN MONTHLY INSTALLMENT (EMI) IS CALCULATED AS
LOAN = A[(1+i)n-1] / i(1+i)n => 330128 = A[ (1 + 5/1200)12x20 -1] / 5/1200(1+5/1200)12x20 (AS R = 5%ANNUAL, N= 12X20)
=> 330128 = A [ (1.0041667)240- 1] / (0.00416670 )(1.0041667)240
=> 330128 = A (2.71264-1) / (0.0041667)( 2.71264)
=> 330128 X 0.004667 X 2.71264 = A (1.71264)
=> 3731.36 /1.71264 =A => A = 2178.72
NOW PROPERTY TAX = 397744 X 2.4% =9545.86 PER YEAR = 795.48/MONTH
HOME OWNER`S INSURANCE = 397744 X 1.3% = 5170.67 PER YEAR = 430.89 PER MONTH
PMI = 68 PER MONTH
HENCE TOTAL MONTHLY COST FOR HOUSE = 2178.72 + 795.48+ 430.89 + 68 = 3473.09
NOW FRONT END RATIO = (TOTAL COST FOR HOUSE PER MONTH) / SALARY PER MONTH MUST BE LESS THAN 28%
HENCE 3473.09 / SALARY < 2 8% => SALARY >(3473.09 X 100) /28 = 12,403.89
AGAIN FOR BANK END RATIO = (TOTAL COST PER MONTH FOR HOUSE + OHTER LOAN INSTALLMENT)/ SALARY < 36%
=> (3473.09+558) / SALARY < 36% => 4031.09/SALARY < 36/100
SALARY > (4031.09 X 100)/36 = 11197.47
HENCE FOR SATISFYING BOTH RULE SIMULTANEOUSLY SALARY MUST BE MORE THAN $ 12403.90
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