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An annuity makes payments for 50 years with the following payment pattern: $1 paid at the end of the first year, $2 at the end of the second year, $1 at the end of the third year, $4 at the end of the fourth year, $1 at the end of the fifth year, etc. This pattern will continue such that $1 will be paid out at the end of the 49th year and $50 will be paid out at the end of the 50th year. What is the present value of this annuity assuming the interest rate is 5% per annum convertible quarterly? A

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Answer:

$154.79

Explanation:

Note: See the attached file for the calculation of the present value of this annuity.

But, we first calculate the effective interest rate as follows:

r = Effective interest rate = (1 + (i/p))^p - 1 .................. (1)

Where;

i = interest rate = 5%, 0.0500

p = number compounding in year = 4

Substituting the values into equation (1), we have:

r = (1 + (0.05/4))^4 - 1 = 0.0509453369140624

Using the effective interest rate above, the present value of this annuity is $154.79.

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