Mary Tsai is paid $16,000 every 30 days. Her salary is deposited initially 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;
4) make any number of evenly spaced withdrawals.
Each withdrawal costs her $3 in terms of time and inconvenience. For each day that Mary has a dollar in the bank, she gets 0.02 cents (0.0002 per dollar) in interest.
1. Create a table showing transaction costs, interest earned, and total net earnings (+) or cost (-) associated with one, two, three, four, and five withdrawals per month.
2. 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?