ou have just won the lottery and you can choose between the following payout opt
ID: 2630613 • Letter: O
Question
ou have just won the lottery and you can choose between the following payout options. The annual interest rate (EAR) is 10%.
a) $100,000 right now and $60,000 every two years starting 3 years from now and ending 17 years from now (i.e., payments are at t = 0, t = 3, t = 5, ... , t = 15, t = 17).
b) $60,000 a year for 25 years with the first payment one year from today (i.e., payments ar e at t = 1, 2, 3 ... 24, 25).
c) 25 annual payments of $45,000 and a 26th payment of $299,000. The first payment is made right now, and the $299,000 payment is made one year after the last $45,000 payment. How much more is the best option worth today relative to the worst option?
Explanation / Answer
a.n = 8, i = (1+10%)2-1 = 21%
PV interest factor = (1-(1+i)-n)/i = (1-(1+21%)-8)/21% = 3.7256
PVa = 100,000 + 60,000*3.7256/(1+10%)2 = $284,739.28
b.n = 25 ,i = 10%
PV interest factor = (1-(1+i)-n)/i = (1-(1+10%)-25)/10% = 9.0770
PVb = 60000*9.0770 = $544,622.40
c.n = 25 ,i = 10%
PV interest factor = (1-(1+i)-n)/i = (1-(1+10%)-25)/10% = 9.0770
PVc = 45000*9.0770*(1+10%) + 299000 * (1+10%)-25 = $476,909.98
The best option is B while tne worst is A
PVb - PVa = $544,622.40 - $284,739.28 = $259,883.12
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