To solve this, let's break it into steps:

Step 1: Find the couple's monthly salary

Their total annual salary is $44,000. To find their monthly salary: $\text{Monthly Salary} = \frac{44,000}{12} = 3,666.67$

Step 2: Determine the maximum allowable monthly house payment

Financial advisors recommend that the house payment should not exceed 25% of the monthly salary. So, we calculate: $\text{Max Monthly House Payment} = 0.25 \times 3,666.67 = 916.67$ This means their maximum allowable monthly house payment is $916.67.

Step 3: Use the payment to find the maximum loan amount for a 30-year and 15-year mortgage

We use the following formula to calculate the loan amount based on the monthly payment: $M = P \frac{r(1+r)^n}{(1+r)^n-1}$ Where:

• $M$ = monthly payment ($916.67),
• $P$ = loan amount (which we are solving for),
• $r$ = monthly interest rate (annual rate divided by 12),
• $n$ = total number of payments (loan term in years multiplied by 12 months).

a) For a 30-year mortgage at 5% interest

• $r = \frac{5\%}{12} = 0.004167$,
• $n = 30 \times 12 = 360$ months.

Now solve for $P$: $916.67 = P \times \frac{0.004167(1+0.004167)^{360}}{(1+0.004167)^{360}-1}$ Let's simplify and solve for $P$: $P = \frac{916.67 \times \left[(1.004167)^{360} - 1\right]}{0.004167(1.004167)^{360}}$

b) For a 15-year mortgage at 5% interest

• $r = 0.004167$,
• $n = 15 \times 12 = 180$ months.

Similar to the previous case, we solve for $P$: $916.67 = P \times \frac{0.004167(1+0.004167)^{180}}{(1+0.004167)^{180}-1}$

I will compute the loan amounts for both cases next.### Results:

• For a 30-year mortgage at 5% interest, the couple qualifies for a maximum loan amount of approximately $170,759.
• For a 15-year mortgage at 5% interest, the couple qualifies for a maximum loan amount of approximately $115,918.

Would you like further details on any part of this process or clarification on the calculations?

Here are some related questions to explore:

1. How would a higher interest rate affect the maximum loan amount?
2. What if the couple could afford 30% of their monthly income for a house payment?
3. How does a 20-year mortgage compare in terms of maximum loan amount?
4. What happens if their combined salary increases to $60,000 per year?
5. How does an adjustable-rate mortgage (ARM) differ from a fixed-rate mortgage?

Tip: When interest rates rise, opting for a shorter mortgage term like 15 years reduces total interest paid, even if the monthly payment is higher!