You can afford a $1200 per month mortgage payment. You've found a 30 year loan at 8% 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?

$


We can solve this mortgage problem using the standard formula for calculating monthly payments on a fixed-rate loan:

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

Where:
- $ M $ is the monthly mortgage payment ($1,200),
- $ P $ is the loan amount (what we want to find),
- $ r $ is the monthly interest rate (8% annually, which is 0.08/12 per month),
- $ n $ is the total number of payments (30 years × 12 months = 360 payments).

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

We will solve for $ P $ using the formula:

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

Now, let's calculate that.

### Part B: How much total money will you pay?

The total amount paid to the loan company is the monthly payment multiplied by the number of payments:

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

### Part C: How much of that money is interest?

The interest is the difference between the total money paid and the principal (loan amount):

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

Let's calculate each of these.### a) The loan you can afford is approximately **$163,540.19**.

### b) The total money you will pay to the loan company over 30 years is **$432,000**.

### c) The total interest paid over the life of the loan is approximately **$268,459.81**.

Would you like more details on these calculations, or do you have any questions?

Here are 5 related questions you could explore:
1. What happens to the loan amount if the interest rate decreases to 6%?
2. How would shortening the loan term to 15 years impact the total interest paid?
3. What is the impact of making additional monthly payments toward the principal?
4. How much equity will you have after 10 years of payments?
5. What is the break-even point when comparing a 30-year mortgage to a 15-year mortgage?

**Tip**: Paying more than the required amount each month can reduce your total interest significantly!

You can afford a $1200 per month mortgage payment. You've found a 30 year loan at 8% 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 $1200 monthly payment on a 30-year loan at 8% interest. Detailed breakdowns of total payments and interest paid. Suitable for high school students and those learning about finance.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation