Financial advisors say that the maximum amount of a person’s house payment (monthly) should be no more than 25% of their monthly salary. If a couple has a total salary of $44,000 per YEAR (divide by 12 to find their monthly salary): ● Determine their maximum monthly house payment allowable; and ● Based on the payment found above, and using an interest rate of 5%, determine the maximum loan amount they qualify for both a (a) 30-year and (b) 15-year mortgage

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!

Financial advisors say that the maximum amount of a person’s house payment (monthly) should be no more than 25% of their monthly salary. If a couple has a total salary of $44,000 per YEAR (divide by 12 to find their monthly salary): ● Determine their maximum monthly house payment allowable; and ● Based on the payment found above, and using an interest rate of 5%, determine the maximum loan amount they qualify for both a (a) 30-year and (b) 15-year mortgage.

This guide explains how to calculate the maximum allowable monthly house payment based on 25% of a couple's salary of $44,000 per year. Learn how to use the loan amortization formula to determine the maximum loan amount for 30-year and 15-year mortgages at a 5% interest rate.

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