Final answer:
Christopher can afford to allocate $900/month towards a home loan payment, allowing us to calculate the total loan amount he can afford over a 30-year period at a 5.9% interest rate using the present value of an annuity formula. Adding his $22,000 down payment to this loan amount gives the maximum price of the house he can purchase.
Step-by-step explanation:
The question asks us to determine how much Christopher can afford to pay for a house, given a maximum monthly payment he can afford for his mortgage and other expenses. To calculate this, we need to account for the monthly portion of his budget that will go towards the loan payment, excluding taxes, insurance, fees, and maintenance. With $1,200 as his maximum monthly spend and $300 going towards other expenses, Christopher has $900 per month available for loan payments. Given that he has a $22,000 down payment, we'll need to calculate the maximum loan amount that a $900 monthly payment can service over a 30-year period at a 5.9% annual interest rate.
Using the present value of an annuity formula, which takes into account the periodic payment amount, the number of periods (months), and the interest rate, we can determine the total loan amount that Christopher can afford. With this loan amount and his down payment, we can then calculate the maximum price of the house he is able to purchase.