Question

14.( )Joe Brady just won a $450,000 lottery in Pennsylvania. Instead of receiving a lump sum, he found that he would receive $22,500 annually (end of year) for 20 years. Joe is 75 years old and wants his money now. He has been offered $140, 827 to sell his ticket. What rate of return is the buyer expecting to make if Joe accepts the offer? a. b. C. d. less than 1% 15% 18% 12%

Answer 1

Here the Present value of the total of 20 annual withdrawals of $22,500 is $140,827 therefore expected rate of return can be calculated with the help of PV of an Annuity formula in following manner

PV = PMT * [1-(1+i) ^-n)]/i

Where,

Present value of amount received by sell of ticket (PV) =$140,827

PMT = Annual payment =$22,500

n = N = number of payments = 20 years

i = I/Y = interest rate per year or rate of return =?

Therefore,

$140,827 = $22,500 * [1- (1+i) ^-20]/i

By trial and error method we got the value of i = 15%

Therefore correct answer is option b. 15%