Multiple choice

Rachel wants to invest in a bond that pays an annual interest rate of 5%, compounded semi-annually. She wants her investment to be at least $3,000 at the end of 2 years. What is the minimum value of her initial investment?

  1. $2,564.50
  2. $2,581.70
  3. $2,602.50
  4. $2,717.85
  5. $2,660.80
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Compound interest formula: A = P(1 + r/n)^(nt). 3000 = P(1 + 0.05/2)^(2*2) = P(1.025)^4. 3000 = P(1.10381289). P = 3000 / 1.10381289 = 2717.85.

AI explanation

Using the compound interest formula A = P(1 + R/100)^n for semiannual compounding, the rate per period is 2.5% and the number of periods is 4. We set up the equation 3000 = P(1 + 2.5/100)^4, which simplifies to P = 3000 / (1.025)^4. Calculating the denominator gives approximately 1.10381289, so P equals 3000 / 1.10381289 which is about 2717.85. The minimum value of her initial investment is $2,717.85.

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