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Assessment Activity 2
Time Value of money - Mortgage
Kyle and Julia are considering whether or not to buy a particular property valued at $720,000. They have $200,000 of their own funds to commit towards the purchase and they expect to incur an additional $50,000 in fees and taxes on the purchase itself. They are able to borrow at an interest rate of 7.20 per cent per annum with interest compounded monthly. Loan repayments would be monthly with the first payment due at the end of the first month after purchasing the property. The term of the home loan is 30 years. They both work full-time earning a combined after-tax salary of $12,000 per month.
Hint: because the interest is compounded monthly, we need to use the number of months for the mortgage loan, not the number of years in determining the regular payments to be made. We also need to use the monthly interest rate (7.2% /12 = 0.6%)
Using the present value of an annuity formula we can rearrange the following formula to obtain the regular monthly mortgage payment PMT.
PV = PMT
PMT = PV /
Alternatively, you can use a financial calculator to determine PMT.
PV = amountborrowed from the bank
r = interest rate per month
n = number of months over the entire loan period
If we select the payment key (PMT) on the financial calculator, we will know the amount of the regular monthly mortgage payments the bank requires us to pay.
2) A loan affordability ratio is equal to the monthly home loan repayment divided by a couple’s household after-tax monthly income. A key threshold for ‘mortgage stress’ is when the loan affordability ratio reaches 35%. Will Kyle and Julia face mortgage stress at current interest rates.
3) After 1 year, the bank informs Kyle and Julia that $564,429 is still owing on their loan. How much in total have Kyle and Julia paid in mortgage payments during the first year?
4) Of the repayments, how much of their principal has been reduced?
5) How much interest have they paid in year 1?
6) If the bank now increases interest rates from 7.20 per cent to 8.40 per cent, what will Kyle and Julia’s new monthly mortgage repayments be?
Hint: remember to use monthly interest rates. And, remember that there are only 29 years left on the loan (use months not years).
7) How will this new monthly mortgage repayment affect their loan affordability ratio? That is, will they be facing mortgage stress?