Final answer:
To find the maximum mortgage amount you can afford with a 30-year fixed-rate mortgage at 7.2% interest with monthly payments of $1,070, you would use the present value of an annuity formula involving the monthly payment, monthly interest rate, and total number of payments. The formula helps calculate the loan principle based on these factors.
Step-by-step explanation:
To calculate the maximum mortgage amount you can afford with a monthly repayment of up to $1,070 at an interest rate of 7.2% over a 30-year fixed-rate mortgage, you can use the formula for the present value of an annuity (loan principle). The formula takes into account the monthly interest rate, the total number of payments (360 for a 30-year loan), and the monthly payment amount.
The monthly interest rate is the annual rate divided by 12 months. In this case, 7.2% annually becomes 0.72 / 12 = 0.006 per month. The formula for the present value of an annuity (PVA) is given by:
PVA = Pmt × [(1 - (1 + r)^-n) / r]
Where:
- Pmt is the monthly payment amount
- r is the monthly interest rate
- n is the total number of payments
Using the information provided:
PVA = $1,070 × [(1 - (1 + 0.006)^-360) / 0.006]
By calculating this, you would arrive at the maximum loan principle you could afford. Keep in mind, this does not account for any down payment, property taxes, insurance, or other costs associated with buying a house.
Since we're not using a calculator here, you would typically employ a financial calculator or a software tool equipped with financial functions to perform this computation.