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Zorluk: OrtaSimple Interest

A retiree wants to earn exactly 1,8001,800 in simple interest over a period of 15 months to help pay for a vacation. A local credit union offers a short-term investment account with an annual simple interest rate of 4%4\%. Assuming no other deposits or withdrawals are made, how much money must the retiree deposit initially to reach this interest goal?

  1. A
    $3,000
  2. B
    $3,600
  3. $36,000Cevap
  4. D
    $45,000

Cevap

$36,000
To find the initial deposit (principal), the simple interest formula I=P×R×TI = P \times R \times T must be rearranged to solve for PP, yielding P=IR×TP = \frac{I}{R \times T}. Because the rate is an annual percentage, the 15-month period must first be converted into years (15/12=1.2515 / 12 = 1.25 years). Substituting the given values gives P=18000.04×1.25P = \frac{1800}{0.04 \times 1.25}, which simplifies to 1800/0.05=360001800 / 0.05 = 36000. Therefore, an initial deposit of 36,00036,000 is required.

Adım Adım Çözüm

1
Convert the time duration from months to years.
T=1512=1.25T = \frac{15}{12} = 1.25 years
The interest rate is provided as an annual rate, so the time factor in the simple interest formula must also be expressed in years.
2
Set up the simple interest formula with the known values.
I=P×R×T→1800=P×0.04×1.25I = P \times R \times T \rightarrow 1800 = P \times 0.04 \times 1.25
The formula connects the interest earned (II) to the principal (PP), rate (RR), and time (TT).
3
Solve for the unknown principal (PP).
P=18000.04×1.25=18000.05=36000P = \frac{1800}{0.04 \times 1.25} = \frac{1800}{0.05} = 36000
Isolating PP determines the initial deposit required to reach the interest goal.

Anahtar Kavram

Calculating the initial principal using the simple interest formula by isolating the principal variable and properly converting time into years.
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Konular

Simple Interest

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