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Sagot :
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.
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.
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