Determine the maximum​ 30-year fixed-rate mortgage amount for which a couple could qualify if the rate is 4.01 percent. Assume they have other debt payments totaling ​$361 per month and a combined annual income of ​$74 comma 800. Monthly escrow payments for real estate taxes and​ homeowner's insurance are estimated to be ​$209. ​(Assume a 36 percent maximum of annual income for total debt and escrow​ payments.)
Question content area bottom
Part 1
The maximum​ 30-year fixed-rate mortgage amount for which a couple could qualify if the rate is 4.01​% is ​$

enter your response here. ​(Round to the nearest​ dollar.)

To determine the maximum mortgage amount for which the couple could qualify, we need to consider the 36% debt-to-income (DTI) ratio, which limits the amount of their income that can go toward paying their debt (including the mortgage, other debt, and escrow payments). Here's how we can break this down:

### Step 1: Determine the Maximum Monthly Payment
The couple's combined annual income is $74,800. The maximum total debt payments allowed (at 36%) are:

\[
\text{Maximum Debt Payments} = 0.36 \times \text{Annual Income}
\]
\[
\text{Maximum Debt Payments} = 0.36 \times 74,800 = 26,928 \, \text{per year}
\]

Now, convert this to a monthly amount:

\[
\text{Maximum Monthly Debt Payments} = \frac{26,928}{12} = 2,244 \, \text{per month}
\]

### Step 2: Account for Other Monthly Payments
The couple has other debt payments of $361 per month and monthly escrow payments (real estate taxes and homeowner's insurance) of $209 per month. So, their non-mortgage payments are:

\[
\text{Non-mortgage Payments} = 361 + 209 = 570 \, \text{per month}
\]

This means the maximum allowable mortgage payment is:

\[
\text{Maximum Monthly Mortgage Payment} = 2,244 - 570 = 1,674 \, \text{per month}
\]

### Step 3: Calculate the Maximum Mortgage Amount
We now need to determine the mortgage amount corresponding to a monthly payment of $1,674, with an interest rate of 4.01% and a 30-year term. We can use the formula for the monthly mortgage payment, which is:

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

Where:
- $ M $ is the monthly mortgage payment ($1,674),
- $ P $ is the loan principal (which we need to solve for),
- $ r $ is the monthly interest rate (annual rate divided by 12, so $ \frac{4.01\%}{12} = 0.00334 $),
- $ n $ is the number of payments (30 years × 12 months = 360).

Rearranging the formula to solve for $ P $:

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

Substituting the values:

\[
P = \frac{1,674 \times \left( (1 + 0.00334)^{360} - 1 \right)}{0.00334 \times (1 + 0.00334)^{360}}
\]

Solving this, the maximum mortgage amount is approximately **$351,560**.

---

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How does the debt-to-income ratio affect mortgage approval?
2. What factors influence the mortgage interest rate a couple might qualify for?
3. How would a higher income or lower debt impact the maximum mortgage amount?
4. What are some strategies for lowering monthly escrow payments?
5. How does a fixed-rate mortgage compare to an adjustable-rate mortgage?

**Tip:** Improving your credit score can lower your interest rate, increasing the mortgage amount you qualify for.

Determine the maximum​ 30-year fixed-rate mortgage amount for which a couple could qualify if the rate is 4.01 percent. Assume they have other debt payments totaling ​$361 per month and a combined annual income of ​$74,800. Monthly escrow payments for real estate taxes and​ homeowner's insurance are estimated to be ​$209. ​(Assume a 36 percent maximum of annual income for total debt and escrow​ payments.)

Learn how to determine the maximum 30-year fixed-rate mortgage for a couple with a combined income of $74,800 and other monthly debts totaling $361. This step-by-step solution covers debt-to-income ratio, interest rate calculations, and loan payment formulas to find a mortgage amount of approximately $351,560.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation