If the cost of going to the ATM is $1 and the nominal interest rate is 5 percent, someone who has a 15 percent probability of having his cash lost or stolen and spends $10 each day will go to the ATM once in every ____ days approximately.
A)10
B)13
C)16
D)19

Question

If the cost of going to the ATM is $1 and the nominal interest rate is 5 percent, someone who has a 15 percent probability of having his cash lost or stolen and spends $10 each day will go to the ATM once in every ____ days approximately. 
A)10
B)13
C)16
D)19

Quizplus · Accepted Answer

The expected loss from theft or loss is 15% of $10, which is $1.50 per day. Adding the ATM cost of $1, the total cost per day is $2.50. With a 5% nominal interest rate, the daily interest rate is approximately 0.05/365 = 0.000137. To find the number of days (n) that minimizes the total cost, we equate the daily cost to the interest cost of holding cash: $2.50 = $10 * n * 0.000137. Solving for n gives approximately 19 days.

If the Cost of Going to the ATM Is $1