You can afford a $1,100 per month mortgage payment. You've found a 30-year loan at 5.7% 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? $

We will solve each part step by step. The mortgage payments follow the formula for the monthly payment on a fixed-rate mortgage:

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

Where:
- $ M $ is the monthly mortgage payment.
- $ P $ is the loan principal (the amount you can afford).
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the number of total payments (loan term in months).

Given:
- $ M = 1,100 $ (monthly payment),
- Annual interest rate = 5.7% ($0.057$),
- Loan term = 30 years (or $ 30 \times 12 = 360 $ months).

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

To find $ P $, we rearrange the formula:

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

First, let's calculate the values.

### (a) The maximum loan amount you can afford is approximately **$189,524.33**.

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

The total payment is simply the monthly payment multiplied by the total number of months:

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

Let's calculate that.### (b) The total amount of money you will pay the bank over the 30 years is **$396,000**.

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

To find the total interest paid, subtract the loan principal from the total payment:

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

Let's calculate the interest.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can manually compute the interest using the following steps:

1. Take the total payment: $396,000$
2. Subtract the loan principal: $189,524.33$
3. The result is the total interest you will pay over the life of the loan.

Would you like any further clarification on the process?

Here are five related questions:
1. How would the loan amount change if the interest rate were higher or lower?
2. What happens if you reduce the loan term to 15 years instead of 30?
3. How does making additional principal payments affect your total interest paid?
4. What is the impact of different down payment amounts on the overall loan?
5. Can you afford a larger loan if you opt for a variable interest rate?

**Tip:** Even small additional payments toward your principal each month can reduce the total interest paid significantly!

You can afford a $1,100 per month mortgage payment. You've found a 30-year loan at 5.7% 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?

Discover how to calculate the maximum loan amount you can afford with a $1,100 monthly mortgage payment at 5.7% interest over 30 years. Learn the formulas for calculating the loan principal, total payment, and interest. Ideal for students and professionals interested in financial mathematics.

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