You can afford monthly payments of ​$400. If current mortgage rates are 3.94​% for a 30​-year fixed rate​ loan, how much can you afford to​ borrow? If you are required to make a 20​% down payment and you have the cash on hand to do​ it, how expensive a home can you​ afford? (Hint: You will need to solve the loan payment formula for​ P.)
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How much can you afford to​ borrow? (Round to the nearest dollar as​ needed.)

To solve this, we can use the mortgage loan payment formula, which is based on the present value of an annuity. The formula is:

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

Where:
- $ M $ is the monthly payment
- $ P $ is the loan principal (the amount you borrow)
- $ r $ is the monthly interest rate (annual rate divided by 12)
- $ n $ is the number of months (loan term in years multiplied by 12)

### Given values:
- $ M = 400 $ (monthly payment)
- Annual interest rate = 3.94%, so monthly interest rate $ r = \frac{3.94\%}{12} = 0.03283\% $
- Loan term = 30 years, so $ n = 30 \times 12 = 360 $ months

We will solve the equation for $ P $, the loan principal.

\[
400 = P \times \frac{0.0394/12 \times (1 + 0.0394/12)^{360}}{(1 + 0.0394/12)^{360} - 1}
\]

Let me calculate the value of $ P $.You can afford to borrow approximately **$84,395**.

### Now, let's calculate the total price of the home you can afford, given that you are required to make a 20% down payment. The loan amount represents 80% of the home's price.

If $ P $ is 80% of the home price, the full price of the home can be calculated as:

\[
\text{Home price} = \frac{P}{0.80}
\]

Let me calculate that for you.You can afford a home priced at approximately **$105,494**, assuming you make a 20% down payment.

Would you like further details on any part of this calculation?

### Related questions:
1. How do mortgage rates impact the loan amount I can afford?
2. What if I wanted a shorter loan term, like 15 years—how would that affect my monthly payments?
3. What would happen if I could afford a higher monthly payment, say $500?
4. How would a change in the down payment percentage impact the total home price I can afford?
5. How do taxes and insurance affect the overall affordability of a mortgage?

### Tip:
Always compare different mortgage rates from lenders to get the best deal, as even small rate changes can significantly affect your affordability.

You can afford monthly payments of ​$400. If current mortgage rates are 3.94​% for a 30​-year fixed rate​ loan, how much can you afford to​ borrow? If you are required to make a 20​% down payment and you have the cash on hand to do​ it, how expensive a home can you​ afford? (Round to the nearest dollar as​ needed.)

Learn how to calculate the loan you can afford with a $400 monthly payment and a 3.94% interest rate for a 30-year fixed mortgage. Discover how to use the loan payment formula and determine the maximum home price, including a 20% down payment. Perfect for financial planning and real estate decisions.

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