The nominal interest rate in an economy is 5 percent, and there is also a 15 percent probability of having cash lost or stolen in the economy.Given this information, what is the cost of going to the ATM for an individual who spends $10 daily and has a total cost of holding cash = (365/T) + T.Assume that the individual visits the ATM once in every T days.
A)$1
B)$2
C)$3
D)$4

Question

Quizplus · Accepted Answer

The cost of going to the ATM is the sum of the cost of holding cash and the probability of losing cash. The cost of holding cash is (365/T) + T, and the probability of losing cash is 15%. So, the cost of going to the ATM is (365/T) + T + 0.15 * 10 = (365/T) + T + 1.5. To minimize this cost, we need to find the value of T that minimizes (365/T) + T + 1.5. Taking the derivative of this expression with respect to T and setting it equal to zero, we get:-365/T^2 + 1 = 0-365 + T^2 = 0T^2 = 365T = sqrt(365) = 19.11So, the individual should visit the ATM once every 19.11 days to minimize the cost of going to the ATM. The cost of going to the ATM is then:(365/19.11) + 19.11 + 1.5 = $20.00

The Nominal Interest Rate in an Economy Is 5 Percent