Question

1. Sue is planning to buy a house. She has been advised by her financial planner that her monthly house payment (which includes property taxes and insurance) should not exceed 30% of her take-home pay. Currently, her take-home pay is $2000 per month. Her monthly property taxes will be approximately $100 and her monthly homeowners insurance will be approximately $50. If Sue’s take-home pay is $2000 per month, and the mortgage is at 0.5% per month for 30 years, what is the maximum amount she can borrow to buy her house?

2. Gary and Ann have just purchased a new home. They paid $40,000 as a down payment and obtained a $200,000 mortgage to pay for the rest. The 30-year mortgage has an interest rate of 0.5% per month. How much will they pay each month in principal and interest? Your answer must be correct to the nearest penny.

Answer 1

Ans 1)

Monthly Income of Sue is $2000 and she should not exceed more than 30% for her monthly house payments

therefore she should not be paying more than 2000*0.3=600

Now she would be paying 100 for proerty tax , 50 for homeowners insurance then she is left with $450 sso that is her ideal EMI as exceeding is not allowed beyond $450

hence with the given EMI of 450 , r=0.5% and T=30*12=360 months

450/(1.005)+...+450/(1.005)^360=450*166.67=75000

Hence she can afford to buy a house worth $75,000 for given terms

Ans 2)

Let the EMI be X

Then using present value criterion we have

X(1/(1.005)+(1/1.005)^2+...(1/1.005)^360)=160000

Now from part 1 we know

(1/1.005)+(1/1.095^2)+...+(1/1.005)^360=166.67

X*166.67=160000

X=160000/166.67=959.988

Hence the EMI is $959.988 per month interest to be paid 160000*0.5%=800 and principal=159.98 interests component decreases month over month and principal component increases month over month.