You can afford a $1450 per month mortgage payment. You've found a 30 year loan at 6% 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?

$

To solve this problem, we need to determine the maximum loan amount you can afford based on a monthly payment of $1,450, a 30-year mortgage, and an annual interest rate of 6%. We will also calculate the total amount paid over the life of the loan and the total interest paid.

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

The monthly mortgage payment formula for a fixed-rate mortgage is given by:

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

where:
- $ M $ is the monthly mortgage payment.
- $ P $ is the principal loan amount (what we are solving for).
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the total number of payments (loan term in years multiplied by 12).

Given:
- $ M = 1450 $
- Annual interest rate $ = 6\% = 0.06 $
- Monthly interest rate $ r = \frac{0.06}{12} = 0.005 $
- Loan term $ = 30 $ years, so $ n = 30 \times 12 = 360 $ months

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

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

Let's calculate the maximum loan amount $ P $. 

\[
P = 1450 \times \frac{(1 + 0.005)^{360} - 1}{0.005 \times (1 + 0.005)^{360}}
\]

Let's compute this.

**Part (a):** The maximum loan amount you can afford is approximately **$241,847.84**.

### Part (b): How much total money will you pay the loan company?

To find the total amount paid over the life of the loan, multiply the monthly payment by the total number of payments:

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

Let's calculate this.**Part (b):** The total amount you will pay the loan company over 30 years is **$522,000**.

### Part (c): How much of that money is interest?

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

\[
\text{Total Interest Paid} = \text{Total Amount Paid} - P
\]

Let's calculate the total interest paid.**Part (c):** The total interest you will pay over the life of the loan is approximately **$280,152.16**.

### Summary
- **Loan amount you can afford:** $241,847.84
- **Total amount paid to the loan company:** $522,000
- **Total interest paid:** $280,152.16

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

Here are 5 related questions you might find useful:
1. How would the loan amount change if the interest rate was lower?
2. What happens to the total interest paid if the loan term is reduced to 15 years?
3. How does making extra payments on the mortgage affect the total interest paid?
4. What would be the effect of increasing your monthly mortgage payment on the loan term?
5. How does a variable interest rate mortgage compare to a fixed-rate mortgage in terms of total payments?

**Tip:** Paying extra on your mortgage principal can reduce the overall interest paid and shorten the loan term.

You can afford a $1450 per month mortgage payment. You've found a 30 year loan at 6% 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?

Determine the maximum loan amount you can afford with a $1450 monthly mortgage payment at 6% interest over 30 years. Learn how to calculate the total payment to the loan company and the total interest paid using key financial formulas.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation