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Question

Difficulty: HardSimple Interest

A small business owner takes out a $12,500\$12,500 personal loan to finance new equipment. The loan agreement specifies an annual simple interest rate of 6.4%6.4\%. If the owner repays the loan in full at the end of 4545 months, what is the total amount that must be repaid?

  1. A
    $12,800\$12,800
  2. B
    $13,300\$13,300
  3. $15,500\$15,500Answer
  4. D
    $16,100\$16,100

Answer

$15,500\$15,500
The correct total amount to repay is found by first converting the 45-month term into years by dividing by 12, which gives 3.75 years. Next, the simple interest is calculated by multiplying the principal ($12,500\$12,500), the annual rate as a decimal (0.0640.064), and the time in years (3.753.75) to get $3,000\$3,000. Finally, adding this interest to the original principal yields the total repayment amount of $15,500\$15,500.

Step-by-Step Solution

1
Convert the loan duration from months to years.
45 months÷12 months/year=3.75 years45 \text{ months} \div 12 \text{ months/year} = 3.75 \text{ years}
The interest rate is an annual rate, so the time period in the formula must be expressed in years.
2
Calculate the total simple interest earned over the period.
I=P×r×t=$12,500×0.064×3.75=$3,000I = P \times r \times t = \$12,500 \times 0.064 \times 3.75 = \$3,000
This determines the additional cost of borrowing the money for the specified time.
3
Add the calculated interest to the original principal to find the total repayment amount.
A=$12,500+$3,000=$15,500A = \$12,500 + \$3,000 = \$15,500
The question asks for the total amount that must be repaid, which includes both the principal balance and the accumulated interest.

Key Concept

To find the total amount to be repaid on a loan, you must calculate the simple interest using the formula I=P×r×tI = P \times r \times t, ensuring the time tt is converted to years, and then add this interest to the principal PP.
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Topics

Simple Interest

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