To determine the amount of money that will be spent in interest alone over the course of a 30-year mortgage with a 5% annual interest rate, we can follow these steps:
### Step 1: Understand the Given Data
From the information provided:
- Principal Amount: [tex]$150,000
- Interest Rate: 5% annually
- Monthly Payment: $[/tex]805
- Loan Term: 30 years
### Step 2: Calculate the Total Number of Monthly Payments
Since the loan term is 30 years and there are 12 months in a year, the total number of monthly payments can be calculated as:
[tex]\[
\text{Total Payments} = 30 \text{ years} \times 12 \text{ months/year} = 360 \text{ payments}
\][/tex]
### Step 3: Calculate the Total Amount Paid Over the Course of the Mortgage
The total amount paid over the course of the loan can be found by multiplying the monthly payment amount by the number of payments:
[tex]\[
\text{Total Amount Paid} = \text{Monthly Payment} \times \text{Total Payments}
\][/tex]
Substituting the given values:
[tex]\[
\text{Total Amount Paid} = 805 \text{ dollars} \times 360 \text{ payments} = 289,800 \text{ dollars}
\][/tex]
### Step 4: Calculate the Interest Paid Alone
The interest paid is the difference between the total amount paid over the life of the loan and the principal amount:
[tex]\[
\text{Interest Paid} = \text{Total Amount Paid} - \text{Principal}
\][/tex]
Substituting the given values:
[tex]\[
\text{Interest Paid} = 289,800 \text{ dollars} - 150,000 \text{ dollars} = 139,800 \text{ dollars}
\][/tex]
### Conclusion
The amount of money that will be spent in interest alone over the course of the 30-year mortgage with a 5% annual interest rate is $139,800.
