Millionaire Life is a promotional lottery game offered across Canada (see Britis
ID: 1101469 • Letter: M
Question
Millionaire Life is a promotional lottery game offered across Canada (see British Columbia Lottery Corporation at www.bclc.com). The prizes included a top prize of $1 million a year for 25 years, four prizes of $1 million, 36 prizes of $100,00, 16 prizes of $1000, and 180,507 prizes of $20. The winner of the top prize had the option of receiving $1 million a year for 25 years or a single lump sum of $17 million. All other prizes were cash prizes. Suppose that the remaining lottery proceeds can be invested to generate an interest rate of 6% per year. If the winner of the top prize selected to receive $1 million a year for 25 years, the first payment occurred right away, and the last payment occurs 24 years later, what is the balance of lottery proceeds right after the last payout? If the winner of the top prize selected to receive a single lump sum of $17 million, what is the balance of lottery proceeds 24 years after this payout?Explanation / Answer
If the winner of the top prize selected to receive $1 million a year for 25 years,
balance, is Future Value of annuity due
1*(1.06^24)+1*(1.06^23+1*(1.06^22)+1*(1.06^21)+1*(1.06^20)+1*(1.06^19)+1*(1.06^18)+1*(1.06^17)+1*(1.06^16)+1*(1.06^15)+1*(1.06^14)+1*(1.06^13)+1*(1.06^12)+1*(1.06^11)+1*(1.06^10)+1*(1.06^9)+1*(1.06^8)+1*(1.06^7)+1*(1.06^6)+1*(1.06^5)+1*(1.06^4)+1*(1.06^3)+1*(1.06^2)+1*(1.06^1)+1*(1.06^0)
= $54.864512 million
or,
the above part can aalso be solved as,
as above is an annuity of 25 years
FV after 25 years i.e FV of annuity due = (1+r)*P*[(1+r)^n-1]/r = 1.06*1*(1.06^25-1)/.06 = $58.1563827
FV immediately after 24 years = 58.1563826/1.06 = $54.864512
b)
FV = 17*1.06^24 = $68.8318889 million