Chapter 4.1, Problem 59E

To determine

To find: The method of payment that is more profitable.

Answer to Problem 59E

The payment method (b) is more profitable.

Explanation of Solution

Given:

The 2 methods of payments are:

(a) One million dollars at the end of the month.

(b) $2^n$ cents on the nth day.

Calculation:

Consider the method of payment given in option (b).

On the 30^th day, the payment received is calculated as follows:

  $\begin{array}{c}{2}^{30}=1,073,741,824cents\\ =\$10,737,418.24\end{array}$

Since the amount paid using option (b) is clearly greater than the one million dollars paid at the end of the month in option (a), the second payment of method is more profitable.