To determine the amount of money spent in interest alone over the course of a 30-year mortgage with a 3% interest rate and a principal of [tex]$200,000.00, we need to follow these steps:
1. Identify the given values:
- Principal amount: $[/tex]200,000.00
- Interest rate: 3%
- Monthly payment: [tex]$843
- Duration of the mortgage: 30 years
2. Calculate the total number of payments:
Since the duration of the mortgage is 30 years and payments are made monthly, the total number of payments is:
\[
\text{Total number of payments} = 30 \text{ years} \times 12 \text{ months/year} = 360 \text{ payments}
\]
3. Calculate the total amount paid over the lifetime of the mortgage:
The total amount paid is the monthly payment multiplied by the total number of payments:
\[
\text{Total amount paid} = \text{Monthly payment} \times \text{Total number of payments} = \$[/tex]843 \times 360 = \[tex]$303,480
\]
4. Determine the interest paid:
The interest paid is the total amount paid minus the principal amount:
\[
\text{Interest paid} = \text{Total amount paid} - \text{Principal} = \$[/tex]303,480 - \[tex]$200,000 = \$[/tex]103,480
\]
Therefore, the amount of money spent in interest alone over the course of the 30-year mortgage at a 3% interest rate is [tex]\(\$103,480\)[/tex].
