Question

What is the value today of an annuity of $5,600 per year, with the first cash flow received three years from today and the last one received 25 years from today? Use a discount rate of 8 percent. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Given annuity of $5,600 per year, with the first cash flow received three years from today and the last one received 25 years from today.

Let us first calculate the value of anuity 2 year from today, so it is now an ordinary annuity with total 23 payment of $5600 with a discount rate of 8%

So Present value of this annuity at year 2 is calculated using formula

PV at year 2 = A*(1 - (1+r)^(-t))/r = 5600*(1 - 1.08^(-23))/0.08 = $58077.93

So value today of annuity = PV at year 2/(1+r)^2 = 58077.93/1.08^2 = $49792.46