What is the value today of $3,200 per year, at a discount rate of 10 percent, if the first payment is received 6 years from today and the last payment is received 20 years from today?

First, we calculate the present value in year 5 of the annuity and then once again calculate the present value of this result to get the value today

Present value an annuity = P*(1-(1+r)^-n)/r

where P = 3200, r = 0.10 and n = 15 payments (from year 6 to year 20)

Present value of the annuity in year 5  = 3200*(1-(1+0.10)^-15/)0.10

Present value of the annuity in year 5 = 3200*(1-1.10^-15)/0.10

Present value of the annuity in year 5 =  24,339.45

Now with  24,339.45 as the FV , we calculate the present value today as

PV today = FV/(1+r)^n  = 24339.45/1.10^5

PV today =15,112.89

Value today =$15,112.89

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