You can afford a $1,500 per month mortgage payment. You've found a 30-year loan at 4.55% 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? $

This problem involves calculating the maximum loan amount you can afford based on a fixed monthly mortgage payment, interest rate, and loan term. We'll use the following mortgage formula to solve for the loan amount:

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

Where:
- $M$ = monthly mortgage payment = $1,500
- $P$ = loan amount (this is what we need to solve for)
- $r$ = monthly interest rate = $\frac{4.55\%}{12} = 0.00379$
- $n$ = total number of payments = $30 \times 12 = 360$ months

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

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

Let's calculate the loan amount.

### (b) How much total money will you pay the bank?
This is simply the total mortgage payments over 30 years:

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

### (c) How much of that money is interest?
The total interest paid is the difference between the total payment and the principal (loan amount):

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

Let's now compute the results.### (a) The maximum loan amount you can afford is approximately **$294,313.55**.

### (b) The total amount you will pay the bank over 30 years is **$540,000**.

### (c) The total interest you will pay over the life of the loan is approximately **$245,686.45**.

Would you like further details on how these values were calculated?

Here are 5 related questions you might find interesting:
1. How would the loan amount change if the interest rate were 5% instead of 4.55%?
2. What if you could afford $2,000 per month—how much bigger a loan could you get?
3. How does making additional principal payments each month affect total interest paid?
4. What happens to the loan amount if the loan term is shortened to 15 years?
5. Can refinancing a loan during the mortgage term save money on interest?

**Tip:** Making extra payments on your mortgage can significantly reduce the amount of interest you pay over time.

You can afford a $1,500 per month mortgage payment. You've found a 30-year loan at 4.55% 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 mortgage loan you can afford with a $1,500 monthly payment and 4.55% interest rate over 30 years. This solution explains the amortization formula, total loan payments, and interest calculations.

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