Cindy wants to buy a house.Her financial advisor told her that the mortgage loan

Question

Cindy wants to buy a house.Her financial advisor told her that the mortgage loan amount should be no more than 80% of the house price. Further, the monthly housing expenses should be no more than 28% of her monthly income She estimates that monthly housing expenses will consist of mortgage installment plus $222 in taxes and insurance. The mortgage will be paid back in 30 years with 360 equal monthly installments starting a month after the loan is taken. Cindy expects to pay an interest rate of 0.5% per month.!f her monthly income is $9816, what is the maximum house price that she can afford while following the advisor's advice? Assume she can pay 20% down payment. Round your answer to the nearest dollar

Explanation / Answer

First we have to calculate the maximum monthly installment of the loan that Cindy can pay

Her monthly income is $9816

Monthly housing expenses = 28% of monthly income = 28% * $9816 = $2,748.48

But this monthly housing expenses are consist of taxes and insurance of $222 per month

Therefore monthly mortgage installment = $2,748.48 -$222 = $2,526.48 per month

Now we know that Cindy can pay maximum $2,526.48 per month for 30 years with 360 equal monthly installments and interest rate is 0.5% per month.

We can use following Present Value of an Annuity formula to calculate the present value of loan

PV of loan = PMT * [1-(1+i) ^-n)]/i

Where,

Present value of loan (PV) =?

Monthly mortgage payments PMT =$2,526.48

Number of installments n =360

Monthly interest rate I =0.5%

Therefore

PV of Loan = $2,526.48* [1- (1+0.5%) ^-360]/0.5%

PV of Loan = $423,502.66

But the loan in only 80% of the price of house and 20% is paid as down payment

Therefore Maximum price of house that Cindy can afford = $423,502.66 / 80%

= $529,378.32

= $529,378 (rounding off to nearest dollar)

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