To determine the maximum 30-year fixed-rate mortgage amount the couple can qualify for, we need to follow these steps:

1. Calculate the maximum allowable monthly debt payment (including escrow)

We are told that the couple can spend up to 36% of their annual income on total debt and escrow payments. Their combined annual income is $72,400.

$\text{Maximum allowable debt and escrow} = 0.36 \times 72,400 = 26,064 \, \text{per year}$

This amount is for a year, so we convert it to a monthly amount:

$\text{Maximum monthly allowable debt and escrow payment} = \frac{26,064}{12} = 2,172 \, \text{per month}$

2. Subtract non-mortgage payments (other debts and escrow)

The couple has other monthly debt payments of $379, and escrow payments for real estate taxes and homeowner's insurance of $251.

So, the total of these non-mortgage payments is:

$379 + 251 = 630 \, \text{per month}$

3. Calculate the maximum monthly mortgage payment

Now, subtract the non-mortgage payments from the total maximum allowable debt and escrow payment to find the maximum allowable mortgage payment.

$\text{Maximum mortgage payment} = 2,172 - 630 = 1,542 \, \text{per month}$

4. Calculate the mortgage amount using the mortgage formula

Now that we know the maximum allowable mortgage payment, we can calculate the total mortgage amount based on a 30-year fixed-rate mortgage at 6.16%.

The mortgage payment formula is:

$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$

Where:

• $M$ is the monthly mortgage payment (1,542)
• $P$ is the loan amount (what we're solving for)
• $r$ is the monthly interest rate (annual rate divided by 12)
• $n$ is the number of payments (30 years × 12 months = 360 months)

First, convert the annual interest rate of 6.16% to a monthly rate:

$r = \frac{6.16}{100 \times 12} = 0.00513$

Now, solve the mortgage formula for $P$:

$P = \frac{M \times \left( (1+r)^n - 1 \right)}{r \times (1+r)^n}$

Substitute the values:

$P = \frac{1,542 \times \left( (1+0.00513)^{360} - 1 \right)}{0.00513 \times (1+0.00513)^{360}}$

Solving this equation, the maximum mortgage amount the couple can qualify for is approximately $256,000.

Final Answer:

The maximum mortgage amount the couple can qualify for is $256,000.

Would you like further explanation or details on any of the steps? Here are a few related questions:

1. How does changing the interest rate affect the mortgage qualification?
2. What would happen if their non-mortgage debt payments increased?
3. How is the mortgage amount affected by a higher escrow payment?
4. What if the couple could allocate more than 36% of their income to debt payments?
5. How would a shorter mortgage term (e.g., 15 years) change the maximum loan amount?

Tip: Increasing your down payment can help lower the loan amount needed and improve your chances of approval.