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Question

Difficulty: EasySimple Interest Applications

Sarah deposits $2,000\$2,000 into a savings account that earns a simple interest rate of 3%3\% per year. If she makes no additional deposits or withdrawals, how much total interest will the account have earned at the end of 4848 months?

  1. A
    $2,880\$2,880
  2. B
    $60\$60
  3. $240\$240Answer
  4. D
    $2,400\$2,400

Answer

$240\$240
To find the simple interest, use the formula I=PRTI = PRT. First, convert the time from months to years by dividing 4848 by 1212, which equals 44 years. Then, multiply the principal ($2,000\$2,000), the annual decimal rate (0.030.03), and the time in years (44). This gives 2000×0.03×4=2402000 \times 0.03 \times 4 = 240. The total interest earned is $240\$240.

Step-by-Step Solution

1
Convert the given time from months into years.
48 months÷12 months/year=4 years48 \text{ months} \div 12 \text{ months/year} = 4 \text{ years}
The interest rate is annual (per year), so the time must also be expressed in years.
2
Convert the percentage interest rate into a decimal.
3%=0.033\% = 0.03
Percentages must be expressed as decimals to be used mathematically in the formula.
3
Calculate the total simple interest using the formula I=PRTI = PRT.
I=2000×0.03×4=240I = 2000 \times 0.03 \times 4 = 240
Multiplying the principal (PP), the rate (RR), and the time (TT) yields the total interest earned over the period.

Key Concept

Calculating simple interest over a multi-year period requiring unit conversion from months to years.
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Topics

Simple Interest Applications

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