The following table shows annual rates for various types of loans in 2015. Assume monthly payments and compounding periods. HINT [See Examples 5 and 7.]
Loan
Type	30-Year
Mortgage	15-Year
Mortgage	5-Year
Car Loan	4-Year
Car Loan	Credit
Cards
October
Rate (%)	3.93	3.14	4.30	4.24	13.10
November
Rate (%)	4.09	3.31	4.31	4.26	13.10
December
Rate (%)	4.09	3.34	4.34	4.29	13.10
You were considering buying a home with a 30-year mortgage in November 2015 and could afford to make a down payment of $50,000 and up to $1400 per month on mortgage payments. How much could you have afforded to pay for the home? (Round your answer to the nearest cent.)

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!

---

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.

You were considering buying a home with a 30-year mortgage in November 2015 and could afford to make a down payment of $50,000 and up to $1400 per month on mortgage payments. How much could you have afforded to pay for the home?

Learn how to calculate the maximum home price you can afford with a 30-year mortgage, a $50,000 down payment, and $1,400 in monthly mortgage payments. This guide walks you through using the mortgage payment formula and converting annual interest rates to monthly rates.

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