The cost of going to an ATM is $2 in an economy.If the nominal interest rate in the economy is 1 percent, what is the total cost associated with holding cash for an individual who spends $15 daily and has a 9 percent probability of having his cash lost or stolen? Assume that he visits the ATM once in every T days.
A)(365/T) + (0.75 × T)
B)(730/T) + (0.75 × T)
C)(730/T) + (1.5 × T)
D)(365/T) + (1.5 × T)

Question

Quizplus · Accepted Answer

The total cost consists of the ATM fee cost and the cost of holding cash. The ATM fee cost is $2 every T days, which annualizes to 365/T * $2 = 730/T. The cost of holding cash includes the interest foregone and the risk of loss or theft. Daily spending is $15, so the average cash holding is $15*T/2 (since cash decreases linearly from $15T to $0 over T days). The interest foregone is 1% of this amount annually, or 0.01 * $15*T/2 = $0.15T/2 = $0.075T. The risk of loss or theft is 9% of the average cash holding, or 0.09 * $15*T/2 = $0.675T. The total cost of holding cash is thus $0.075T + $0.675T = $0.75T. Therefore, the total cost is (730/T) + (0.75 × T).

The Cost of Going to an ATM Is $2 in an Economy.If