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Difficulty: MediumSimple Interest Applications

To purchase a used vehicle, a buyer finances $12,000\$12,000 through a dealership. The financing agreement includes an annual simple interest rate of 6.5%6.5\%. If the buyer pays off the loan over a period of 4242 months, what is the total amount repaid at the end of the financing period?

  1. A
    $2,730\$2,730
  2. B
    $12,780\$12,780
  3. $14,730\$14,730Answer
  4. D
    $15,276\$15,276

Answer

The total amount repaid is $14,730\$14,730.
The correct answer is derived by first converting the 4242-month term into 3.53.5 years. Applying the simple interest formula (I=PRTI = PRT), the total interest is calculated as $12,000×0.065×3.5=$2,730\$12,000 \times 0.065 \times 3.5 = \$2,730. Finally, the interest is added to the principal to find the total repayment: $12,000+$2,730=$14,730\$12,000 + \$2,730 = \$14,730.

Step-by-Step Solution

1
Convert the loan duration from months to years.
42 months=4212=3.5 years42 \text{ months} = \frac{42}{12} = 3.5 \text{ years}.
The interest rate given is annual, so the time variable must be expressed in years.
2
Calculate the total simple interest accrued using the formula I=PRTI = PRT.
I=$12,000×0.065×3.5=$2,730I = \$12,000 \times 0.065 \times 3.5 = \$2,730.
This determines the cost of borrowing the money over the specified time period.
3
Add the interest to the original principal to find the total repayment amount.
Total Amount = $12,000+$2,730=$14,730\$12,000 + \$2,730 = \$14,730.
The buyer must repay both the original loan amount and the accumulated interest.

Key Concept

Calculating the total maturity value using simple interest by correctly converting months to years and adding the accrued interest to the principal.
Estimated Time:1m 15s
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Topics

Simple Interest Applications

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