Question

# 1. Suppose you have a 20 percent probability of having your cash lost or stolen, and...

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?

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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