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To solve this problem, we will use the loan payment formula:

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

where:
- $ M $ is the monthly payment ($800 in this case),
- $ P $ is the loan principal (the amount you can borrow, which we need to find),
- $ r $ is the monthly interest rate (annual rate divided by 12),
- $ n $ is the total number of payments (years of the loan multiplied by 12).

### Given Data:
- Monthly payment, $ M = 800 $
- Annual interest rate, $ r_{\text{annual}} = 4.24\% = 0.0424 $
- Loan term, $ n_{\text{years}} = 30 $

### Step 1: Convert Annual Interest Rate to Monthly Rate
\[
r = \frac{0.0424}{12} = 0.0035333
\]

### Step 2: Calculate the Number of Payments
\[
n = 30 \times 12 = 360
\]

### Step 3: Solve for $ P $ in the Loan Payment Formula
Rearranging the formula to solve for $ P $:
\[
P = \frac{M \times \left((1 + r)^n - 1\right)}{r \times (1 + r)^n}
\]

### Step 4: Substitute the Values
\[
P = \frac{800 \times \left((1 + 0.0035333)^{360} - 1\right)}{0.0035333 \times (1 + 0.0035333)^{360}}
\]

Let’s compute this value:

\[
P \approx \frac{800 \times (3.530 - 1)}{0.0035333 \times 3.530}
\]
\[
P \approx \frac{800 \times 2.530}{0.01248}
\]
\[
P \approx \frac{2024}{0.01248}
\]
\[
P \approx 162,145
\]

So, you can afford to borrow approximately **$162,145**.

### Step 5: Consider the Down Payment
If a 10% down payment is required:
\[
\text{Total Home Price} = \frac{P}{0.9} = \frac{162,145}{0.9} \approx 180,161
\]

Thus, the most expensive home you can afford is approximately **$180,161**.

Would you like more details or have any questions?

### Related Questions:
1. What if the mortgage rate was 5% instead of 4.24%?
2. How does the loan amount change if you extend the loan to 40 years instead of 30?
3. What would the monthly payment be if you borrowed $200,000 at the same rate?
4. How much more expensive of a home can you afford if your monthly payment limit is $1,000 instead of $800?
5. What is the impact of increasing the down payment to 20% on the total home price?

### Tip:
Always calculate the total loan cost by considering the interest paid over the loan term. It helps to evaluate the long-term financial commitment.

You can afford monthly payments of $800. If current mortgage rates are 4.24% for a 30-year fixed-rate loan, how much can you afford to borrow? If you are required to make a 10% down payment and you have the cash on hand to do it, how expensive a home can you afford?

Learn how to calculate the amount you can afford to borrow for a 30-year fixed-rate mortgage with a 4.24% interest rate and a monthly payment of $800. This solution explains the loan payment formula and includes a 10% down payment requirement.

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