You can afford a $950 per month mortgage payment. You've found a 30 year loan at 7% interest.

a) How big of a loan can you afford

To determine the maximum loan amount you can afford given a $950 monthly payment, a 30-year term, and a 7% annual interest rate, we will rearrange the mortgage payment formula to solve for the loan principal $ P $:

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

Here:
- $ M $ is the monthly payment: $950
- $ r $ is the monthly interest rate: $\frac{7\%}{12} = \frac{0.07}{12} \approx 0.0058333 $
- $ n $ is the number of monthly payments: $30 \text{ years} \times 12 \text{ months/year} = 360 \text{ months}$

### Step-by-Step Calculation:

1. **Convert the monthly payment formula to solve for $ P $:**
\[ P = \frac{M (1 + r)^n - 1}{r (1 + r)^n} \]

2. **Plug in the values:**
\[ P = \frac{950 \left[(1 + 0.0058333)^{360} - 1\right]}{0.0058333 (1 + 0.0058333)^{360}} \]

### Calculating the Loan Principal:

First, we need to calculate $(1 + r)^{360}$:
\[ (1 + 0.0058333)^{360} \approx 10.677 \]

Now plug this value into the formula:
\[ P = \frac{950 \left[10.677 - 1\right]}{0.0058333 \times 10.677} \]

\[ P = \frac{950 \times 9.677}{0.062296} \]

\[ P = \frac{9,193.15}{0.062296} \]

\[ P \approx 147,588 \]

### Maximum Loan Amount:

The maximum loan amount you can afford with a $950 monthly payment, a 30-year term, and a 7% annual interest rate is approximately $ \$147,588 $.

Would you like any more details or have any questions?

Here are 5 numbered questions for you to ask:
1. How do I calculate the total interest paid over the life of a loan?
2. What are the advantages of a shorter loan term versus a longer one?
3. How do changes in the interest rate affect the maximum loan amount I can afford?
4. What factors should I consider when choosing between different mortgage options?
5. How can I improve my credit score to get a better mortgage rate?

**Tip:** Consider using an online mortgage calculator to quickly estimate loan amounts, monthly payments, and the impact of different interest rates and loan terms.

Discover how to calculate the maximum loan amount you can afford with a $950 monthly payment, 30-year term, and 7% interest rate. Detailed step-by-step solution using mortgage payment formulas and compound interest calculations.

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