Mary Tsai Is Paid $3,000 Every 30 Days

Essay

Mary Tsai is paid $3,000 every 30 days. Her salary is deposited directly in her bank. She spends all her money at a constant rate over the 30 days and must pay cash. She can (1) withdraw all of the money at once; (2) withdraw half at once and the rest after 15 days; (3) withdraw one-third at once, one-third after 10 days, and one-third at 20 days; or (4) make any number of evenly spaced withdrawals. Each withdrawal costs her $2 in terms of time and inconvenience. For each day that Mary has a dollar in the bank, she gets .03 cents (.0003 per dollar) in interest. Thus, if she withdraws half of her money immediately and half in 15 days, she has $1,500 in the bank for 15 days and earns $6.75 interest.
a. Create a table showing transaction costs, interest earned, and total net earnings (+) or cost (-) associated with one, two, three, or four withdrawals per month.
b. How many withdrawals per month lead to the largest net earnings? If Mary chooses this number, what will be her average amount of cash on hand over the 30 days?