Question

You have just won the initial School of Finance lottery! You have won $10,000 today, $20,000 four years from today, and $30,000 six years from today. As an alternative, you can receive your winnings as a 10-year annuity with the first payment received ten years from today. If you require a 6% return on your investment, how much must the annuity pay you each year for you to select that option?

Answer 1

Given about a Lottery,

payments are $10000 today, $20000 4 years from today and $30000 six years from today.

interest rate = 6%

calculating total future value of these cash flow 10 year from now using formula Fv = PV*(1+r)^t

So, Total future value = 10000*1.06^10 + 20000*1.06^6 + 30000*1.06^4 = $84153.17

Now this future payment is like present value for an annuity due that starts paying at start of each year for next ten years. formula used to calculated PMT of this annuity is

PMT = PV*r/((1+r)*(1 - (1+r)^(-t))) = 84153.17*0.06/(1.06*(1 - 1.06^-10)) = $10786.53

So, annuity payment that starts 10 years from now for the lottery is $10786.53