You can afford a $1300 per month mortgage payment. You've found a 30 year loan at 7% interest. 

a) How big of a loan can you afford? Round your answer to the nearest dollar.

$

b) How much total money will you pay the loan company? Round your answer to the nearest dollar.

$Correct

c) How much of that money is interest? Round your answer to the nearest dollar.

To solve this problem, we need to use the formula for the monthly mortgage payment of a loan. The formula is:

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

Where:
- $ M $ is the monthly mortgage payment ($1300 in this case).
- $ P $ is the loan amount (what we want to find).
- $ r $ is the monthly interest rate (7% annual rate = $ 0.07/12 $ per month).
- $ n $ is the total number of payments (30 years = $ 30 \times 12 = 360 $ months).

### Step (a): Calculate the loan amount $ P $.

Rearranging the formula to solve for $ P $:

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

Now, let's calculate it.

First, let's define:
- $ M = 1300 $
- $ r = \frac{0.07}{12} = 0.0058333 $
- $ n = 30 \times 12 = 360 $

I'll compute $ P $.(a) The maximum loan you can afford is approximately **$195,400**.

### Step (b): Calculate the total amount paid over the life of the loan.

The total payment is the monthly payment times the number of months:

\[
\text{Total Payment} = M \times n = 1300 \times 360
\]

Let me calculate this.(b) The total amount you will pay over the life of the loan is **$468,000**.

### Step (c): Calculate how much of the total payment is interest.

The interest paid is the total payment minus the loan amount:

\[
\text{Interest} = \text{Total Payment} - P
\]

Let me calculate the interest.(c) The total interest you will pay over the life of the loan is approximately **$272,600**.

Would you like more details or have any questions?

### Related Questions:
1. How would the loan amount change if the interest rate were 6% instead of 7%?
2. What if the loan term were reduced to 20 years instead of 30 years?
3. How much would you save in interest if you made an extra $100 payment each month?
4. How much equity would you build after 10 years of payments?
5. How would a down payment affect the size of the loan?

**Tip:** Making extra payments early in the loan can significantly reduce the total interest paid.

You can afford a $1300 per month mortgage payment. You've found a 30-year loan at 7% interest.

a) How big of a loan can you afford? Round your answer to the nearest dollar.

b) How much total money will you pay the loan company? Round your answer to the nearest dollar.

c) How much of that money is interest? Round your answer to the nearest dollar.

Find out how large of a loan you can afford with a $1300 monthly payment on a 30-year mortgage at 7% interest. Learn how to calculate the total amount paid over the life of the loan and how much of that will go towards interest. Ideal for students in Grades 11-12 or college-level financial mathematics.

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