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Difficulty: MediumSimple Interest

A civil engineer needs to earn exactly $840\$840 in simple interest over a 1010-month period to offset the cost of new drafting software. If a local credit union offers a business savings account with a 4.8%4.8\% annual simple interest rate, how much principal must be deposited into the account?

  1. A
    $1,750\$1,750
  2. B
    $2,100\$2,100
  3. C
    $17,500\$17,500
  4. $21,000\$21,000Answer

Answer

The correct principal amount to deposit is $21,000\$21,000.
The correct answer accurately uses the simple interest formula by first converting the 10-month period into a fraction of a year (10/1210/12 or 5/65/6). Multiplying the annual rate of 0.0480.048 by 5/65/6 yields 0.040.04. Dividing the target interest of $840\$840 by 0.040.04 correctly determines the required principal.

Step-by-Step Solution

1
Identify the known variables from the problem.
Interest (II) = $840\$840, annual rate (rr) = 4.8%=0.0484.8\% = 0.048, and time (tt) = 1010 months.
Organizing the given information clarifies what is needed for the simple interest formula.
2
Convert the time period from months to years because the interest rate is an annual rate.
t=1012=56 yearst = \frac{10}{12} = \frac{5}{6} \text{ years}
Standard simple interest formulas require time to be in the same unit as the rate.
3
Substitute the values into the simple interest formula I=P×r×tI = P \times r \times t to set up the equation.
840=P×0.048×56840 = P \times 0.048 \times \frac{5}{6}
This establishes the mathematical relationship to isolate the unknown principal amount (PP).
4
Simplify the equation and solve for the principal.
840=P×0.04⇒P=8400.04=21000840 = P \times 0.04 \Rightarrow P = \frac{840}{0.04} = 21000
Dividing both sides by the calculated coefficient isolates PP and yields the final answer.

Key Concept

Solving for Principal using the Simple Interest Formula
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Topics

Simple Interest

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