Question

21. Suppose you are offered a job that lasts one month. Which of the following methods of payment do you prefer?

I. One million dollars at the end of the month.

II. One cent on the first day of the month, two cents on the second day, four cents on the third day, and, in general, \({2^{n - 1}}\) cents on the \(n{\bf{th}}\) day.

Short answer

The payment in plan II should be preferred as it results in a larger payment than that in the plan I.

Step-by-step solution

Analyze the situation given in II

Let the last month of work be February, so there are 28 days in February.

Thus, according to the payment plan in II, the payment on the 28^th day is shown below:

\(\begin{aligned}{2^{28 - 1}} &= {2^{27}}\\ &= \$ 1,342,177.28\end{aligned}\)

Thus, the payment is $1,342,177.28.

Compare the situation in II with that in I

The payment in plan I is fixed to 1 million dollars, whereas in plan II, it results in greater than 1 million dollars for February.

It will result in a much larger payment at the end of the month as the number of days in any month is more significant than that in February.

Draw a conclusion

The payment in plan II should be preferred as it results in a larger payment than that in the plan I.