You have just won the Georgia Lottery with a jackpot of $26,000,000. Your winnings will be paid to you in 26 equal annual installments with the first payment made immediately. If you had the money now, you could invest it in an account with a quoted annual interest rate of 8% with monthly compounding of interest. What is the present value of the stream of payments you will receive?
Given about a lottery,
Amount paid = $26000000 in 26 equal annual installment
So, equal installment = 26000000/26 = $1000000 per year start today
interest rate APR = 8% per year compounded monthly
So, effective annual rate = (1 + APR/n)^n - 1
For monthly compounding, n = 12
=> Effective annual rate r = (1 + 0.08/12)^12 - 1 = 8.30%
So, Present value of this annuity is calculated using PV formula of an annuity due
Present value = PMT*(1+r)*(1 - (1+r)^-t)/r = 1000000*1.083*(1-1.083^-26)/0.083 = $11406850.80
So, present value of the stream of payments is $11406850.80
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