To find out how much money will be spent in interest alone over the course of the [tex]$4 \%$[/tex] 30-year mortgage, we need to understand a few key pieces of information:
1. Principal Amount: This is the initial loan amount, which is \[tex]$120,000.
2. Monthly Payment: For a $[/tex]4 \%[tex]$ interest rate, the monthly payment is \$[/tex]573.
3. Loan Term: The mortgage is for 30 years.
Here is a step-by-step breakdown of the solution:
1. Calculate the total amount paid over the mortgage term:
- We know that there are 12 months in a year.
- The loan term is 30 years.
- Multiplying these together, we find that there are [tex]\(30 \times 12 = 360\)[/tex] monthly payments in total.
Hence, the total amount paid over 30 years is:
[tex]\[
360 \text{ payments} \times \$573 \text{ per payment} = \$206,280
\][/tex]
2. Calculate the total interest paid:
- The total amount paid over the life of the mortgage includes both the principal and the interest.
- Subtract the initial loan amount (principal) from the total amount paid to find the total interest paid.
[tex]\[
\text{Total Interest Paid} = \$206,280 - \$120,000 = \$86,280
\][/tex]
Thus, the amount of money spent in interest alone over the course of the [tex]$4 \%$[/tex] 30-year mortgage is [tex]$\$[/tex]86,280$.
