Sure! Let's go through the solution step-by-step.
1. Identify the initial cost of the truck:
The initial cost, or principal, of the truck is [tex]$42,500.
2. Determine the interest rate and the loan term:
The interest rate is 3.75%, which we can write as a decimal (0.0375).
The loan term is 7 years.
3. Calculate the total interest paid over the loan term:
Interest is calculated using the simple interest formula: \( I = P \times r \times t \)
- \( P \) is the principal amount ($[/tex]42,500)
- [tex]\( r \)[/tex] is the annual interest rate as a decimal (0.0375)
- [tex]\( t \)[/tex] is the time in years (7)
Plugging in these values:
[tex]\[
I = 42,500 \times 0.0375 \times 7
\][/tex]
The total interest paid over the 7 years is [tex]$11,156.25.
4. Calculate the total amount paid:
To determine the total amount Sharon will pay by the end of the loan term, we add the total interest to the initial cost of the truck.
\[
\text{Total amount paid} = \text{Principal} + \text{Total interest}
\]
\[
\text{Total amount paid} = 42,500 + 11,156.25
\]
The total amount paid is $[/tex]53,656.25.
So, at the end of the 7 years, Sharon will have paid a total of $53,656.25 for the truck.
