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Difficulty: MediumSimple Interest Applications

A small business owner finances the purchase of new office equipment with a $3,000\$3,000 loan from a local credit union. The loan term is 1818 months. At the end of the term, the owner repays a total of $3,360\$3,360, which includes the original loan amount and all accumulated simple interest.

What is the annual simple interest rate (as a percentage) applied to this loan?

Answer: 8 %

Answer

8
The correct annual simple interest rate is 8%. First, determine the total interest by subtracting the principal from the total repayment ($3,360−$3,000=$360\$3,360 - \$3,000 = \$360). Next, convert the 18-month term to years (18÷12=1.5 years18 \div 12 = 1.5 \text{ years}). Using the simple interest formula I=PRTI = PRT, substitute the values: 360=3,000×R×1.5360 = 3,000 \times R \times 1.5. Simplifying this gives 360=4,500R360 = 4,500R, which means R=360÷4,500=0.08R = 360 \div 4,500 = 0.08. Finally, convert 0.080.08 to a percentage to get 8%8\%.

Step-by-Step Solution

1
Calculate the total simple interest earned over the loan term.
Total Interest (I) = $3,360−$3,000=$360\$3,360 - \$3,000 = \$360
The total repayment amount (A) is the sum of the principal (P) and the interest (I). Therefore, subtracting the principal from the total repayment isolates the interest.
2
Convert the loan duration from months to years.
Time (T) = 18 months=1.5 years18 \text{ months} = 1.5 \text{ years}
The standard simple interest formula I=PRTI = PRT requires time (T) to be expressed in years when calculating an annual interest rate.
3
Apply the simple interest formula and solve for the annual rate (R).
360=3000×R×1.5360 = 3000 \times R \times 1.5
360=4500×R360 = 4500 \times R
R=0.08R = 0.08
Substituting the known values (I, P, T) allows us to isolate and solve for the missing rate variable (R).
4
Convert the decimal rate into a percentage.
0.08=8%0.08 = 8\%
Interest rates are universally expressed as percentages in financial contexts.

Key Concept

Calculating an unknown annual interest rate using the simple interest formula I = PRT, which requires determining the total interest from a final balance and converting time from months to years.
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Topics

Simple Interest Applications

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