Determine the maximum​ 30-year fixed-rate mortgage amount for which a couple could qualify if the rate is 6.16 percent. Assume they have other debt payments totaling ​$379 per month and a combined annual income of ​$72 comma 400. Monthly escrow payments for real estate taxes and​ homeowner's insurance are estimated to be ​$251. ​(Assume a 36 percent maximum of annual income for total debt and escrow​ payments.)

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.

Determine the maximum 30-year fixed-rate mortgage amount for which a couple could qualify if the rate is 6.16 percent. Assume they have other debt payments totaling $379 per month and a combined annual income of $72,400. Monthly escrow payments for real estate taxes and homeowner's insurance are estimated to be $251. (Assume a 36 percent maximum of annual income for total debt and escrow payments.)

Learn how to calculate the maximum mortgage amount a couple can qualify for based on a 6.16% interest rate, $72,400 annual income, $379 monthly debt payments, and $251 in monthly escrow. Detailed step-by-step solution with financial formulas included. Suitable for high school students studying financial math.

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