Final answer:
The present value of an annuity that pays four annual payments of $100, starting three years from now at an interest rate of 12%, is calculated to be approximately $232 when factoring in the two years of discounting before the first payment. However, this value is not listed among the options provided.
Step-by-step explanation:
To determine the present value of an annuity with four annual payments of $100 beginning three years from now at an annual interest rate of 12%, we will use the present value of an annuity formula. We don't have the specific table from the textbook, so we will calculate the present value using the formula itself:
PV = PMT × [(1 - (1 + r)^(-n)) / r]
Where PV is the present value, PMT is the annual payment ($100), r is the annual interest rate (12%, or 0.12), and n is the number of payments (4).
However, we must take into account that the first payment is received three years from now, so we have to discount the result we get once more for those two years that precede the first payment.
First, we calculate the present value of the annuity as if the first payment was received today:
PV = $100 × [(1 - (1 + 0.12)^(-4)) / 0.12]
PV = $100 × [(1 - (1 + 0.12)^(-4)) / 0.12] ≈ $100 × 2.91 = $291
Next, we must discount this amount for the two years before the first payment to find its value three years from now:
PV(today) = $291 / (1 + 0.12)^2 ≈ $291 / 1.2544 ≈ $232
This indicates that the present value of the annuity is approximately $232, which is not listed among the provided options a) to d). It seems there might be a discrepancy or the table in the textbook must be used for an exact value, which we do not have access to currently.