Question

Ou 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:
month 1: $1000
month 2: $1000
month 3: $1000

Method 2:
month 1: $100
month 2: $200
month 3: $300

Method 3:
month 1: $0.01
month 2: $0.02
month 3: $0.04

Decide which number of months will give you the biggest cumulative payout for each method; check all that apply.

a) For months 22 through 30 choose Method 3
b) For months 20 through 21 choose Method 3
c) For the first 19 months choose Method 1
d) For months 22 through 30 choose Method 1
e) For the first 18 months choose Method 2
f) For months 20 through 21 choose Method 2

Answer 1

For the biggest cumulative payout, choose Method 1 for the first 19 months, Method 3 for months 22 through 30, and it varies for months 20 and 21 based on specific calculations not provided here. Method 3 takes advantage of geometric progression to eventually offer the highest payouts after enough time has passed. Method 3 is the correct answer.

Step-by-step explanation:

To determine which payment method provides the biggest cumulative payout, it's essential to analyze the growth patterns of each method over various time spans. Method 1 offers a stable $1000 per month. Method 2 increases by $100 each month, starting from $100. Method 3 doubles every month, starting from $0.01. Calculations are simplified here for clarity.

For Method 3, the amount doubles every month so by the 22nd month, the payout would exponentially surpass that of the other two methods due to the power of geometric progression. Hence, for months 22 through 30, choosing Method 3 would give the biggest cumulative payout.

For Methods 1 and 2, as long as the doubling effect of Method 3 has not surpassed their total, they would be more beneficial. Therefore, for the first 19 months, Method 1 is the best as it provides a consistent high monthly payment. For months 20 and 21, Method 2 begins to catch up, but the exponential growth of Method 3 still doesn't take over until after the 21st month.