You can afford a $1300 per month mortgage payment. You found a 30 year loan at 7% interest. How big of a loan can you afford? How much total money will you pay the loan company and how much of that money is interest?

To find out how big of a loan you can afford with a $1300 per month mortgage payment at 7% interest for 30 years, we need to use the formula for the monthly payment on a fixed-rate mortgage:

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

Where:
- $M$ is the monthly mortgage payment ($1300),
- $P$ is the loan principal (the amount you want to find),
- $r$ is the monthly interest rate (annual interest rate divided by 12),
- $n$ is the total number of payments (loan term in months, which is 30 years × 12 months/year = 360 months).

Let's break it down:
- The annual interest rate is 7%, so the monthly interest rate $r$ = $ \frac{7\%}{12} = \frac{0.07}{12} \approx 0.005833$.
- The total number of payments $n = 30 \times 12 = 360$.

Now we can rearrange the mortgage formula to solve for the loan principal $P$:

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

I'll calculate this step-by-step.The maximum loan you can afford with a $1300 monthly payment at a 7% interest rate over 30 years is approximately **$195,400**.

### Total Amount Paid
To calculate the total amount you'll pay over the life of the loan, simply multiply the monthly payment by the total number of payments:

\[
\text{Total Paid} = M \times n
\]

Let me calculate the total payment and the interest paid.The total amount you'll pay over the life of the loan is **$468,000**.

Of this amount, **$272,600** will be interest.

### Summary:
- Loan amount (principal): **$195,400**
- Total payments: **$468,000**
- Total interest paid: **$272,600**

Would you like more details or have any questions? 

Here are 5 related questions you might consider:
1. How would the loan change if the interest rate were lower, say 5%?
2. What if you could afford a $1500 monthly payment instead?
3. How does the loan term affect the total interest paid?
4. What would happen if you made extra payments each month?
5. How do taxes and insurance typically impact your mortgage payments?

**Tip:** If you make extra payments toward the principal, you can reduce the total interest paid over the life of the loan significantly.

Find out how big of a loan you can afford with a $1300 monthly mortgage payment at 7% interest for 30 years. Calculate the loan principal, total payment amount, and interest paid with step-by-step solutions. Perfect for high school students or financial learners.

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