1. Someone who visits the ATM once every 8 days, and who spends $25 per day. What is his average cash balance?

2. Someone who visits the ATM once every 7 days, and who has an average cash balance of $70. How much does this person spend per day?

3. 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?

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

5. Suppose someone's cost of going to the ATM is $1.50, there is a 12 percent probability of having his cash lost or stolen, and he spends $5 each day. Suppose his total cost of holding cash = (547.50/T) + (0.375 × T). Find the nominal interest rate.

6. If the nominal interest rate is 3 percent and the cost of going to the ATM is $1.50, someone who has a 12 percent probability of having his cash lost or stolen and has the total cost of holding cash = (547.50/T) + (0.375× T). How much does he spend per day?

7. 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. How often will he go to the ATM (in days)?

8. If the cost of going to the ATM is $2 and the nominal interest rate is 1 percent, someone who has a 9 percent probability of having his cash lost or stolen and spends $15 each day. How often will he go to the ATM (in days)?

9. Suppose the nominal interest rate is 3 percent, the cost of going to the ATM is $1.50, you have a 12 percent probability of having your cash lost or stolen, and you spend $5 each day.a. What is your total cost of holding cash as a function of the number of days between trips to the ATM?b. How often will you go to the ATM to minimize your costs?10. 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?