Final answer:
Brandon should calculate the maximum amount he can afford for a monthly mortgage payment by using the present value of an annuity formula with the given affordability of $1,000 per month, a 4.2% annual interest rate, and a 30-year mortgage term. This will ensure he does not take on more debt than he can manage, which is crucial for long-term financial stability.
Step-by-step explanation:
The question is focused on calculating the maximum monthly mortgage payment Brandon can afford and the total amount payable over the term of a 30-year mortgage at an annual interest rate of 4.2%, given that Joanna can afford to pay $12,000 a year for a house loan. To determine the maximum loan Brandon can afford, we will use the present value of an annuity formula, considering the yearly affordability is given as $12,000, which breaks down to monthly affordability by dividing by 12 ($1,000 per month). As the interest rate is annual, for monthly calculations it needs to be divided by 12 (0.35% per month) and the number of payments over 30 years will be 360 (12 months times 30 years).
To solve for the maximum loan amount, the present value annuity formula is:
PV = PMT × ((1 - (1 + r)^-n) / r)
Where PV is the present value (maximum loan amount), PMT is the monthly payment ($1,000), r is the monthly interest rate (0.35%), and n is the total number of payments (360).
Given this information, Brandon can calculate the maximum loan he can afford. Additionally, by multiplying the monthly payment by the number of payments (360), he can determine the total amount he will end up paying after 30 years. Understanding these calculations is crucial to avoid taking on more debt than he can manage, as evidenced by the example of a $1,000,000 loan resulting in over $2.1 million paid after 30 years, or the significant savings achieved by making slightly higher monthly payments on a $300,000 loan.