Question

1. Suppose you have a 20 percent probability of having your cash lost or stolen, and you spend $25 each day. Your total cost of holding cash is (182.50/T) + (3.75 × T).
a. What is your cost of going to the ATM?
b. What is the nominal interest rate?
c. How often will you go to the ATM to minimize your costs?

Answer 1

a) The TC=  cost of going to the ATM +  the opportunity cost of lost interest + the loss from theft,

total cost = (365 * ATM cost) / T + (25 * i * T) / 2 + (25 * T * 20%) /2

= (365 * ATM cost) / T + (12.5 * i + 2.5) * T

Since we know that the TC is

182.5 / T + 3.75 * T

We must have:

365 * ATM cost = 182.5

ATM cost = 0.5

b) We also have:

3.75 = 12.5 * i + 2.5

1.25 = 12.5 * i

i = 10 percent

now , the nominal interest rate is 10 percent

c) The optimal T is given by:

182.5/ T²=3.75

T=7

That is, you go to the ATM every week.

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