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What is the present value of a four-year annuity of $100 per year that makes its first payment 2 years from today if the discount rate is 9%?Question 2Select one:a.$297.22b.$323.97c.$356.85d.$272.68e.None of these solutions is correct

Question

What is the present value of a four-year annuity of 100peryearthatmakesitsfirstpayment2yearsfromtodayifthediscountrateis9100 per year that makes its first payment 2 years from today if the discount rate is 9%?Question 2Select one:a.297.22b.323.97c.323.97c.356.85d.$272.68e.None of these solutions is correct

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Solution

To calculate the present value of an annuity, we use the formula:

PV = PMT * [(1 - (1 + r)^-n) / r]

Where:

  • PV is the present value
  • PMT is the annuity payment
  • r is the discount rate
  • n is the number of periods

However, since the first payment is not made immediately but 2 years from today, we need to discount the calculated present value further for 2 years.

Step 1: Calculate the present value of the annuity as if it were paid starting today:

PV = 100 * [(1 - (1 + 0.09)^-4) / 0.09] = $323.97

Step 2: Discount this present value back 2 years at the discount rate of 9%:

PV = 323.97 / (1 + 0.09)^2 = $272.68

So, the present value of this annuity is 272.68.Therefore,thecorrectanswerisd.272.68. Therefore, the correct answer is d. 272.68.

This problem has been solved

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