Millionaire life is a promotional lottery game offered across Canada. The prizes
ID: 1101465 • Letter: M
Question
Millionaire life is a promotional lottery game offered across Canada. The prizes included a top prize of $1 million a year for 25 years, four prize of $1 million, 36 prize of $100,000, 16 prizes of $1000, and 180,507 prizes of $20. The winner of the top prize had the option of reciving $1 million a year for 25 years or a single lump sum of $ 17 million. All other prizes were cash prize. suppose that the remaining lottery proceeds can be invested to generate an interest rate of 6% per year.
(a) If the winner of the top prize selected to receive $1 million a year for 25 years, the first payment occurred right a way , the last payment occure 24 years later, what is the balance of lottery proccds right after the last payout?
(b) 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
b)
FV = 17*1.06^24 = $68.8318889 million