You and your significant other are contemplating the purchase of a home. Your co

Question

You and your significant other are contemplating the purchase of a home. Your combined family income is $80,000 per year. You know that mortgage lenders use a rule of thumb that the limit on the size of a mortgage loan is that no more than 30% of a family's income should go to the payment of principal and interest. What is the maximum purchase value of a home that you and your partner could purchase assuming that you have a 10% down payment through savings? Assuming one annual mortgage payment instead of 12 monthly payments per year, answer this question for these four cases:

i) 20-year amortization

ii) 30-year amortization

iii) mortgage interest rate of 7%

iv) mortgage interest rate of 11%

(I think it's saying, for example, case 1 20-year amortization with 7% interest, case 2 20-years with 11% interest, etc.)

Explanation / Answer

Case 1 : 20 year amortisation with 7% interest

The maximum installment per year can be 30% of family income which is $24,000 ($80,000*30%) in this case. Thus for calculating maximum paurchase value of home, firstly we have to calculate present value of all the annual installments over 20 years which is calculated as follows:-

PV of annual installments = $24,000*PVAF(7%,20yrs) = $24,000*10.594 = $254,256

This amount of $254,256 must be 90% of the total purchase value as there is a down payment of 10% through savings. Thus the maximum purchase value of home is :-

$254,256/90% = $282,507 (rounded off)

Case 2 : 20 year amortisation with 11% interest

Similarly as per case 1 we will first calculate the PV of annual installments over 20 years but with 11% interest rate.

PV of Annual Installments = $24,000*PVAF(11%,20yrs) = $24,000*7.963 = $191,112

Maximum Purchase value = $191,112/90% = $212,347 (rounded off)

Case 3 : 30 year amortisation with 7% interest

In this case we will calculate PV of annual payments over 30 years with 7% interest rate.

PV of Annual Installments = $24,000*PVAF(7%,30 yrs) = $24,000*12.409 = $297,816

Maximum Purchase Value = $297,816/90% = $330,907

Case 4 : 30 year amortisation with 11% interest

In this case we will calculate PV of annual payments over 30 years with 11% interest rate.

PV of Annual Installment = $24,000*PVAF(11%,30 yrs) = $24,000*8.694 = $208,656

Maximum Purchase Value of Home = $208,656/90% = $231,840

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