To determine how much home you could afford with a 30-year mortgage, we'll use the following details:

• Down payment: $50,000
• Maximum monthly payment: $1,400
• Interest rate for a 30-year mortgage in November 2015: 4.09%
• Loan term: 30 years (360 months)

We will use the monthly payment formula for a fixed-rate mortgage:

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

Where:

• $M$ is the monthly payment ($1,400),
• $P$ is the loan amount (what we need to find),
• $r$ is the monthly interest rate (annual interest rate divided by 12),
• $n$ is the number of monthly payments (360 months for a 30-year mortgage).

Step 1: Convert the interest rate to a monthly rate.

The annual rate is 4.09%, so the monthly interest rate is:

$r = \frac{4.09\%}{12} = \frac{0.0409}{12} = 0.00340833$

Step 2: Plug the known values into the formula and solve for $P$.

We know that $M = 1,400$, $r = 0.00340833$, and $n = 360$. Now we solve for $P$.

$1,400 = \frac{P \cdot 0.00340833 \cdot (1 + 0.00340833)^{360}}{(1 + 0.00340833)^{360} - 1}$

This simplifies into a more complex algebraic expression. Let me solve it for you.The maximum loan amount you could afford based on a $1,400 monthly payment and a 30-year mortgage at a 4.09% interest rate is approximately $290,084.23.

Step 3: Add the down payment.

Since you can afford a $50,000 down payment, the total home price you could afford is:

$\text{Total Home Price} = \text{Loan Amount} + \text{Down Payment} = 290,084.23 + 50,000 = 340,084.23$

Thus, you could afford to pay approximately $340,084.23 for the home.

Let me know if you want more details or have any questions!

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Here are 5 related questions for deeper understanding:

1. How would the result change if the interest rate had been 5%?
2. What would your monthly payment be for a 15-year mortgage at the same loan amount?
3. How much would you have saved in interest with a 15-year mortgage?
4. How does the amortization schedule impact early vs. later payments?
5. What are the tax implications of making a larger down payment?

Tip: When considering mortgage options, always compare how different rates and terms affect both your monthly payment and the total cost over time.