Question

1. Suppose the nominal interest rate is 3 percent, the cost of going to the ATM is $1.50, you have a 12 percent probability of having your cash lost or stolen, and you spend $5 each day.
a. What is your total cost of holding cash as a function of the number of days between trips to the ATM?
b. How often will you go to the ATM to minimize your costs?

Answer 1

Let the number of Times an ATM is visited be T

Cost of going to ATM =(365*1.50)/T

Opportunity Cost = (5*0.03*T)/2

Expected Cost of Loss = (5*T*0.12)/2

a.Total Cost = (365*1.50)/T+(5*0.03*T)/2+(5*T*0.12)/2

Using the minimisation function we get

b. 38 days

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