You can afford a $1,350 per month mortgage payment. You've found a 30-year loan at 4.6% interest.

(a) How big of a loan can you afford? $

(b) How much total money will you pay the bank? $

(c) How much of that money is interest? $

To solve this mortgage problem, we can use the formula for the monthly payment on a fixed-rate mortgage:

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

Where:
- $M$ is the monthly mortgage payment ($1,350).
- $P$ is the loan principal (what we need to find).
- $r$ is the monthly interest rate, which is the annual rate divided by 12 (4.6% annually = 0.003833 monthly).
- $n$ is the total number of payments (30 years × 12 months/year = 360 months).

### (a) How big of a loan can you afford?
We rearrange the formula to solve for $P$:

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

Substituting the given values:

\[
M = 1350, \quad r = \frac{4.6\%}{12} = 0.003833, \quad n = 360
\]

I’ll calculate this to find $P$.(a) The maximum loan you can afford is approximately **$263,340.45**.

Next, let’s calculate the total amount of money you will pay over the entire loan term.

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

I'll compute that now.(b) The total amount of money you will pay the bank over 30 years is **$486,000**.

Now, to find how much of that total is interest, we subtract the loan amount from the total payments:

\[
\text{Total interest} = \text{Total payments} - P
\]

I'll compute that next.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can calculate the interest by subtracting the loan amount $ P $ from the total amount paid:

\[
\text{Total Interest} = 486,000 - 263,340.45
\]

That should give you the total interest paid.

Let me know if you'd like more details on this or have other questions!

Here are 5 related questions to deepen your understanding:
1. What is the difference between a fixed-rate and adjustable-rate mortgage?
2. How does the length of a loan impact total interest paid?
3. How would a lower interest rate affect the size of the loan you can afford?
4. What is the benefit of making extra payments on your mortgage?
5. How does a down payment affect the total loan amount?

**Tip:** Even small reductions in your interest rate or making extra payments early in your mortgage can significantly reduce the total interest paid.

You can afford a $1,350 per month mortgage payment. You've found a 30-year loan at 4.6% interest. (a) How big of a loan can you afford? (b) How much total money will you pay the bank? (c) How much of that money is interest?

Learn how to calculate the maximum loan you can afford with a $1,350 monthly payment over a 30-year period at 4.6% interest. This guide breaks down the loan amortization formula, total payments, and interest costs. Suitable for Grades 10-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation