Final answer:
To find the annual effective interest rate for the given perpetuity, the formula for present value of a perpetuity is used, but the resulting interest rate does not match any of the provided options.
Step-by-step explanation:
The student has asked to calculate the annual effective rate of interest when the present value of a perpetuity paying $11 at the end of every 4 years is $0.82. To solve for the interest rate, we can use the formula for the present value of a perpetuity:
PV = ∞/ (1 + i)^t
Since the perpetuity is paid every 4 years, we need to find the equivalent annual effective interest rate (i). This is achieved by rearranging the present value formula for perpetuities:
PV = R / i
Where R is the payment every 4 years, and PV is the present value of those payments. Plugging the values we have:
0.82 = 11 / (i * 4)
Solving this equation for i gives:
i = 11 / (0.82 * 4)
i = 11 / 3.28
i = 3.3537, which is equivalent to 335.37% every 4 years
The annual effective rate can be calculated by taking the 4th root of (1 + i) - 1:
Annual rate = ((1 + 3.3537)^(1/4)) - 1
Annual rate ≈ 0.5151 or 51.51%
However, since this result does not match any of the given options, it indicates that there may have been a miscalculation or misunderstanding in the question or the provided answer choices. Therefore, under these circumstances, the correct option is not available.