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The present value of a perpetuity paying 11 at the end of every 4 years is 0.82. Find the annual effective rate of interest.

A. 5.51%
B. 22.06%
C. 33.09%
D. 31.51%
E. 8.82%

1 Answer

6 votes

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.

User Wael Dalloul
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