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 297.22b.356.85d.$272.68e.None of these solutions is correct
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.
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