A 6-year annuity with twelve semiannual payments of $7.000 will begin 11 years f

Question

A 6-year annuity with twelve semiannual payments of $7.000 will begin 11 years from now, with the first payment coming 11.5 years from now If the discount rate is 11 percent compounded monthly, what is the value of this annuity five years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g. 32.16.) Value of the annuity If the discount rate is 11 percent compounded monthly, what is the value three years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g.. 32.16.) Value of the annuity If the discount rate is 11 percent compounded monthly, what is the current value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e-g., 32.16.) Value of the annu

Explanation / Answer

Solution:

First of all we need to compute EAR = (1+0.11/12)^12 - 1 = 11.57% per annum

Then I/n = 11.57/2 = 5.785%

Now, we need to compute the Present value of ordinary annuity(i.e. Pv of annuity at 11years from now)

   PVOA = $7,000{1-(1+0.5785)^-12} / 0.5785 = $59,384.877

Now we can compute all the required PV of annuitiy given in the question by discounting above PVOA as per requirement as follows:

(1)Value of annuity 5 years from now(i.e.6years away from above PVOA at 11 years) = $59,384.877/(1.05785)^12 = $30,240.35 ( Rounded off )

(2) Value of annuity 3 years from now (i.e. 8years away from above PVOA at 11 years)= $59,384.877/(1.05785)^16 = $24,148.51

(3) Current value of annuity (i.e. 11 years away from above PVOA) = $59,384.877/(1.05785)^22= $17,232.40

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