You can afford a $900 per month mortgage payment. You've found a 30 year loan at 7% interest. 2) now big of a loan can you afford? b) How much total money will you pay the loan company? c) How much of that money is interest?

To solve this mortgage problem, we can break it down into three parts.

### Part A: Loan Amount (How big of a loan can you afford?)

The mortgage payment formula (for fixed payments) is based on the formula for the present value of an annuity:

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

Where:
- $ M $ is the monthly mortgage payment (in this case, \$900)
- $ P $ is the loan principal (the amount you can borrow, which we need to find)
- $ r $ is the monthly interest rate, which is the annual rate divided by 12 (so, $ 7\% $ annual interest becomes $ 0.07/12 \approx 0.005833 $)
- $ n $ is the total number of payments, which is $ 30 \times 12 = 360 $ payments over 30 years.

We need to rearrange the formula to solve for $ P $:

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

### Part B: Total Money Paid Over 30 Years

The total amount of money you will pay the loan company is simply the monthly payment multiplied by the number of payments:

\[
\text{Total payments} = M \times n = 900 \times 360
\]

### Part C: Total Interest Paid

The total interest paid is the difference between the total amount paid and the original loan principal:

\[
\text{Total interest} = \text{Total payments} - P
\]

Let’s calculate each of these values.### Results:
1. **Loan Amount (How big of a loan can you afford?)**: You can afford a loan of approximately **$135,276.81**.
   
2. **Total Money Paid Over 30 Years**: The total amount you will pay the loan company over 30 years is **$324,000**.

3. **Total Interest Paid**: The total amount of interest you will pay over the course of the loan is approximately **$188,723.19**.

Would you like more details or further explanations?

Here are 5 related questions to expand on this topic:
1. How would the loan amount change with a 6% interest rate instead of 7%?
2. What would happen if the loan term was 15 years instead of 30 years?
3. How much would you need to pay monthly to afford a $200,000 loan?
4. What is the impact of making extra payments on the loan?
5. How would different types of loans (e.g., adjustable-rate mortgages) affect your payments?

**Tip**: Paying extra toward your principal early in the loan can significantly reduce the total interest paid over time.

You can afford a $900 per month mortgage payment. You've found a 30-year loan at 7% interest. a) How big of a loan can you afford? b) How much total money will you pay the loan company? c) How much of that money is interest?

Learn how to calculate the loan amount you can afford with a $900 monthly mortgage payment, a 30-year term, and 7% interest. Find out how much you’ll pay in total over the life of the loan and how much of that is interest. This problem covers annuities, loan amortization, and interest rates.

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