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 annuity

Explanation / Answer

Nominal Discount Rate = 11 % compounded monthly

Effective Annual Yield = EAY = [1+ (11/1200)]^(12) - 1 = 0.1157 or 11.57 % approximately.

Applicable Half-Yearly Discount Rate = (1.1157)^(1/2) - 1 = 0.05628 or 5.628 % approximately.

(a) Annuity Durateion = 6 years, Annuity Payments = $ 7000 per half-year and first payment starts at t = 11.5 years.

The present value is being asked five years from now which is at the end of Year 5.

Therefore, annuity PV at the end of year 11 = PV(11) = 7000 x (1/0.05628) x [1-{1/(1.05628)^(12)}] = $ 59903.88 approximately.(The value is $ 59902.53 if the discount rate is taken as the rounded value of 5.628 %. However as intermediate rounding is not allowed in this problem, EXCEL calculator has been used to provide a more accurate number).

PV of the annuity at the end of Year 5 = PV(5) = 59903.88 / (1.05628)^(12) = $ $ 31053.19

(b) PV(11) = $ 59903.88

Present Value of the annuity at the end of Year 3 (3 years from now) = PV(3) = 59903.88 / (1.05628)^(16) = $ 24945.37

(c) PV(11) = $ 59903.88

Present Value of the annuity at current time ( end of Year 0) = PV(0) = 59903.88 / (1.05628)^(22) = $ 17960.39

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