Grades
People
Syllabus
Modules
Google Drive
Office 365
19 You can afford a $\$ 1050$ per month mortgage payment. You've found a 30 year loan at $7 \%$ 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?

Step 1 ：Given that the monthly payment is $1050, the annual interest rate is 7%, and the loan term is 30 years, we need to find out the loan amount, the total money paid to the loan company, and the total interest paid.

Step 2 ：First, we convert the annual interest rate to a monthly interest rate by dividing it by 12. This gives us a monthly interest rate of approximately 0.005833333333333334.

Step 3 ：Next, we calculate the number of payments by multiplying the loan term in years by 12. This gives us a total of 360 payments.

Step 4 ：We then use the formula for calculating the loan amount based on the monthly payment, interest rate, and loan term. The formula is: \(\text{Loan Amount} = \frac{\text{Monthly Payment}}{r(1 - (1 + r)^{-n})}\), where r is the monthly interest rate and n is the number of payments. Substituting the given values into the formula, we find that the loan amount is approximately $205,293.34.

Step 5 ：To find the total money paid to the loan company, we multiply the monthly payment by the number of payments. This gives us a total of $378,000.

Step 6 ：Finally, we calculate the total interest paid by subtracting the loan amount from the total money paid to the loan company. This gives us a total interest paid of approximately $172,706.66.

Step 7 ：\(\boxed{\text{Final Answer:}}\) a) The loan amount you can afford is approximately \$205,293.34. b) The total money you will pay the loan company is \$378,000. c) The total interest paid is approximately \$172,706.66.