You have won a contest. You will get to choose one of three methods for payment of your prize. Each method will be paid on a monthly basis. You will be asked to draw a number between 1 and 30. This number will represent the number of months you will be paid your winnings. You must be prepared to identify which of the three payment methods you want at that point. The three methods are:
Method 1 Method 2 Method 3
month 1: $1000 month 1: $100 month 1: $0.01
month 2: $1000 month 2: $200 month 2: $0.02
month 3: $1000 month 3: $300 month 3: $0.04
month 4: $1000 month 4: $400 month 4; $0.08
etc. etc. etc.
Answer these questions:
a. Calculate what the payment would be for the twelfth month for each method.
b. Calculate what the total amount of the prize money would be for 12 months for each method.
c. Decide which method of payment you want and explain why for any given number of months drawn?
d. How many months will it take for your method of choice to pay off more total prize money than the other methods?
e. How much would your total prize money be at this point?

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rendon020996 rendon020996 · Answer 1 · 2020-03-07T02:50:30+01:00

Answer:

a. Calculate what the payment would be for the twelfth month for each method:

b. Calculate what the total amount of the prize money would be for 12 months for each method.

c. Decide which method of payment you want and explain why for any given number of months drawn?

The third method for 30moths, because it's the method that pay off more total prize money than the other methods.

d. How many months will it take for your method of choice to pay off more total prize money than the other methods?

24 months

e. How much would your total prize money be at this point?

$ 10737418.2

Step-by-step explanation:

a. Calculate what the payment would be for the twelfth month for each method:

Method 1: In this method the monthly payment is $1000 and it is a constant payment. This means it doesn't increase each month. Therefore the twelve payment would be $1000
Method 2: In this method the initial payment is $100 but every month the payment increases $100. So for the twelve month the payment would be $1200
Method 3: In this method the initial payment is $0.01 and each month the payment is doubled with respect to the previous month. For example the fifth month the payment would be:

[tex]Fifth payment= (0.08*2)=0.16[/tex]

b. Calculate what the total amount of the prize money would be for 12 months for each method.

Method 1: If each monthly payment is $1000, during 12 months, the total amount would be:

[tex]Method _1 =12*1000=12000[/tex]

Method 2: If each month the payment increases $100. The sum of 12 months, would be:

[tex]Method_2=100+200+300+400+500+600+700+800+900+1000+1100+1200=7800[/tex]

[tex]Method_3=0.01+0.02+0.04+0.08+0.16+0.32+0.64+1.28+2.56+5.12+10.24+20.48=40.95[/tex]

c. Decide which method of payment you want and explain why for any given number of months drawn?

The third method increases exponentialy, the first method stay constant each month and the second method has a linear incrementation.

d. How many months will it take for your method of choice to pay off more total prize money than the other methods?

You can see it on the Excel table added

e. How much would your total prize money be at this point?

As the payment increase exponentially the total amount is: $ 10737418.2