Question

1. If the nominal interest rate is 5 percent, someone who has a 15 percent probability of having his cash lost or stolen and who spends $10 each day, and who has the total cost of holding cash = (365/T) + T. What is the cost of going to the ATM of this person?

Answer 1

Total Cost = cost of going to the ATM + opportunity cost + expected cost of loss or theft

(365/T)+ T = (365 x ATM cost)/T + ($10 x T x nominal interest rate 'i')/2 + ($10 x T x probability of lost or stolen)/2

T means Total annual cost of withdrawing when spending i.e $10

(365/10)+ 10 = (365 x ATM cost) / 10 + (10 x 10 x 0.05)/2 + (10 x 10 x 0.15)/2

46.5 = (36.5 x ATM cost) + 2.5 + 7.5

36.5 = 36.5 x ATM cost

ATM cost = $1

Answer: cost of going to the atm to this person is $1.