Are you better off playing the lottery or saving the money

Assignment Help Corporate Finance

Reference no: EM13381735

Are you better off playing the lottery or saving the money? Assume you can buy one ticket for $5, draws are made monthly, and a winning ticket correctly matches 6 different numbers of a total of 49 possible numbers.

The probabilities: In order to win, you must pick all the numbers correctly. Your number has a 1 in 49 chance of being correct. Your second number, a 1 in 48 chance, and so on. There are exactly 49 x 48 x 47 x 46 x 45 x 44 = 10,068,347,520 ways to pick 6 numbers from 49 options.

But the order in which you pick them does not matter, so you actually have a few more ways to win. You can pick 6 different numbers in exactly 6 x 5 x 4 x 3 x 2 x 1 = 720 orders of choice. Any one of those orders would still win the lottery.

Putting this all together, your ticket has 720/10,068,347,520 = 1/13,983,816 chance of winning. This equates to a .000000071 percentage chance.

If you played one ticket every month from age 18 to age 65, you would have 47 x 12 = 564 plays. Your odds of not ever winning would be calculated using a binomial distribution to be .9999599568, meaning your chances of winning would be 1 - .9999599568 = .0000400432.

So, if the lottery winnings averaged $10 million over this time period, your expected return would be less than .0000400432 x $10 million = $400.43.

(It's less than $400.43 because your 564 plays are spread out over the next 47 years, so the present value of these future plays would be significantly less than if you were able to play all 564 immediately. The $400.43 assumes you play all 564 plays today, which makes it the highest possible expected value.)

REQUIRED:

A. What would your $400.43 be worth if you invested it at 1% real interest for 47 years?

B. If, instead, you wrote down your 6 numbers on a piece of paper, and deposited your $5 in a bank at 1% real interest, how much would you have at the end of the first year?

C. If you did this every year for 47 years, how much would you have at age 65?

D. If you earned 5% real interest on your deposits, how much would you have at age 65?

E. Which option would make you better off at age 65? How many times better off?

Reference no: EM13381735

Questions Cloud

Lasting impressions company lasting impressions li company : lasting impressions company lasting impressions li company is a medium-sized commercial printer of promotional

A large national mco recently entered a major southwestern : a large national mco recently entered a major southwestern metropolitan market. the managed care plan anticipated that

1 sixty-five years old ashley taylor has received 300000 as : 1. sixty-five years old ashley taylor has received 300000 as a lump sum pension settlement. she has invested the money

You and your friends are thinking about starting a : you and your friends are thinking about starting a motorcycle company named apple valley choppers. your initial

Are you better off playing the lottery or saving the money : are you better off playing the lottery or saving the money? assume you can buy one ticket for 5 draws are made monthly

Linus is 18 years old now and is thinking about taking a : linus is 18 years old now and is thinking about taking a 5-year university degree. the degree will cost him 25000 each

Assume you have 1 million now and you have just retired : assume you have 1 million now and you have just retired from your job. you expect to live for 20 years and you want to

General battery company gbc is formulating plans to open : general battery company gbc is formulating plans to open battery exchange centers throughout the u.s. where

Problem 1 what is the price of a bond that has the : problem 1 what is the price of a bond that has the following characteristics a years until maturity 20 b coupon

User Account

All Pages