You can afford a $1350 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 these questions, we'll use the formula for calculating the monthly mortgage payment of a loan (known as the **amortization formula**), which is given by:

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

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

### Given Data:
- Monthly Payment, $ M = 1350 $
- Annual Interest Rate, $ r = 6\% $ (which is $ 0.06 $ as a decimal)
- Loan Term, $ n = 30 $ years

Let's calculate each part step-by-step.

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

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

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

Let's calculate $ P $ using the given values.### a) How Big of a Loan Can You Afford?

The maximum loan you can afford with a monthly payment of $1,350 at a 6% interest rate for 30 years is approximately **$225,169**.

### b) How Much Total Money Will You Pay the Loan Company?

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

\[
\text{Total Paid} = M \times n
\]It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can explain how to calculate the total amount you will pay to the loan company:

### b) Total Money Paid to the Loan Company

The formula to find the total money paid over the life of the loan is:

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

where $ M = 1350 $ (monthly payment) and $ n = 360 $ (total number of payments for 30 years). You can calculate it by multiplying these two numbers:

\[
\text{Total Paid} = 1350 \times 360
\]

### c) How Much of That Money Is Interest?

To find out how much of the total amount paid is interest, subtract the principal (the loan amount calculated in part a) from the total paid:

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

You can use the value of $ P $ from part (a) and the total amount paid from part (b) to calculate the interest.

Would you like to proceed with these calculations manually, or do you have any other questions?

### Additional Questions:
1. What is the effect of increasing the loan term on the interest paid?
2. How would a different interest rate affect the loan amount you can afford?
3. How do extra monthly payments impact the total interest paid over the loan term?
4. What is the difference between a fixed-rate and an adjustable-rate mortgage?
5. How does the down payment affect the size of the loan you can afford?

**Tip:** Understanding how to use the amortization formula can help you better plan and make informed decisions when considering different loan terms and interest rates.

Learn how to calculate the size of a loan you can afford with a $1350 monthly mortgage payment, a 30-year term, and a 6% interest rate. This guide covers key concepts such as the amortization formula, total payment calculation, and interest paid, suitable for students in Grades 10-12.

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