A 10year annuity of 20 8900 semiannual payments will begin 1

A 10-year annuity of 20 $8,900 semiannual payments will begin 11 years from now, with the first payment coming 11.5 years from now. If the discount rate is 8 percent compounded semiannually, what is the value of this annuity ten years and eight years from now? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) What is the value of the annuity today?

Solution

The question is based on the time value of money. Step-1:Calculation of Value of annuity 11 years from now Present value of annuity 11 years from now = Annuity x Present Value of annuity of 1 = $             8,900 x 13.59033 = $ 1,20,953.90 Working: Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.04)^-20)/0.04 i 8%/2 = 0.04 = 13.59033 n 10*2 = 20 Step-2:Calculation of Value of annuity 10 years from now Present Value = Above Value x Discount factor = $ 1,20,953.90 x (1.04^-2) = $ 1,11,828.68 Step-3:Calculation of value of annuity 8 years from now Present Value = Above Value x Discount factor = $ 1,11,828.68 x (1.04^-4) = $     95,591.63 Step-4:Calculation of Value of annuity today Value of annuity today = Above Value x Discount factor = $     95,591.63 x (1.04^-16) = $     51,037.15 Thus Present Value of annuity Value of annuity ten years from now $ 1,11,828.68 Value of annuity eight years from now $     95,591.63 Value of annuity today $     51,037.15