Question
\( \times \) 8) Reggie's automobile service club charged him \( 6.5 \% \) on a car loan. If he borrows \( \$ 2,250 \) for three years, how much will he owe altogether?
Ask by Hodges Christensen. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Reggie will owe a total of \$2,688.75.
Solution
**Step 1: Identify the Variables**
Let
\( P = \$2250 \) (principal),
\( r = 6.5\% = 0.065 \) (annual interest rate in decimal), and
\( t = 3 \) years.
**Step 2: Calculate the Interest Using the Simple Interest Formula**
The formula for simple interest is:
\[
I = P \times r \times t
\]
Substitute the values:
\[
I = 2250 \times 0.065 \times 3
\]
First, calculate \( 2250 \times 0.065 \):
\[
2250 \times 0.065 = 146.25
\]
Now, multiply by 3:
\[
146.25 \times 3 = 438.75
\]
So, the interest is \( I = \$438.75 \).
**Step 3: Calculate the Total Amount Owed**
The total amount owed is the sum of the principal and the interest:
\[
\text{Total} = P + I = 2250 + 438.75 = 2688.75
\]
Thus, Reggie will owe a total of \( \$2688.75 \).
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Simplify this solution Extra Insights
To calculate the total amount Reggie will owe after borrowing \( \$2,250 \) at a \( 6.5\% \) interest rate for three years, we first find the interest amount. The formula for interest is: \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \] Plugging in the values: \[ \text{Interest} = 2250 \times 0.065 \times 3 \] \[ \text{Interest} = 2250 \times 0.195 = 436.25 \] Now, we add the interest to the principal to find the total amount owed: \[ \text{Total Amount} = \text{Principal} + \text{Interest} \] \[ \text{Total Amount} = 2250 + 436.25 = 2686.25 \] So, Reggie will owe \( \$2,686.25 \) altogether.
