You can afford a $1200 per month mortgage payment. You've found a 30 year loan at 6.9% interest.

a) How big of a loan can you afford? (Round to the nearest cent, as needed.)

$


b) How much total money will you pay the loan company? (Round to the nearest cent, as needed.)

$


c) How much of that money is interest? (Round to the nearest cent, as needed.)

$


This is a problem involving mortgage payments, where we are given a monthly payment, loan duration, and interest rate, and we need to determine:

- The size of the loan you can afford.
- The total money you will pay over the life of the loan.
- The amount paid in interest.

Let's solve these step by step.

### Part a: How big of a loan can you afford?

We use the formula for the monthly payment of a mortgage:

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

Where:
- $ M $ is the monthly payment (\$1200).
- $ P $ is the loan principal (the amount we want to find).
- $ r $ is the monthly interest rate (annual rate divided by 12). In this case, $ 6.9\% $ annually is $ 0.069 / 12 = 0.00575 $.
- $ n $ is the total number of payments (loan term in months). For 30 years, $ n = 30 \times 12 = 360 $ months.

Rearranging the formula to solve for $ P $:

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

Substituting the values:

\[
P = \frac{1200 \cdot \left( (1 + 0.00575)^{360} - 1 \right)}{0.00575 \cdot (1 + 0.00575)^{360}}
\]

Calculating this gives us the size of the loan $ P $.

### Part b: Total money paid to the loan company

The total money paid is the monthly payment multiplied by the number of payments:

\[
\text{Total paid} = M \times n = 1200 \times 360 = 432,000
\]

### Part c: Amount of money paid in interest

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

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

Let me compute these values.### Solutions:

a) The size of the loan you can afford is **\$182,204.64**.

b) The total money you will pay to the loan company over the 30 years is **\$432,000.00**.

c) The total amount paid in interest is **\$249,795.36**.

Let me know if you'd like further details or have any questions.

Here are some related questions for further exploration:
1. How would the loan size change with a 5% interest rate?
2. What would happen if the loan term was reduced to 15 years?
3. How much would you save in interest by making extra payments?
4. How does the interest rate impact the overall cost of the loan?
5. What is the impact of increasing the monthly payment by \$100?

**Tip**: Even a small extra payment each month can significantly reduce the total interest paid over the life of the loan!

You can afford a $1200 per month mortgage payment. You've found a 30-year loan at 6.9% interest.

a) How big of a loan can you afford? (Round to the nearest cent, as needed.)

b) How much total money will you pay the loan company? (Round to the nearest cent, as needed.)

c) How much of that money is interest? (Round to the nearest cent, as needed.)

Learn how to calculate the maximum loan size you can afford with a $1200 per month mortgage payment at a 6.9% interest rate over 30 years. Includes step-by-step formulas for determining loan principal, total payments, and interest paid. Suitable for college-level financial math.

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