Ordering Transactions to Avoid Overdraft
At the start of the term, the student council bank account has $245. Five transactions are scheduled: a fundraiser deposit of $180, a $95 payment for supplies, a $140 bus deposit, a $75 printing bill, and a $60 donation. The bank charges a $35 overdraft fee whenever the balance is negative at the end of any transaction, with one fee per transaction. The treasurer can choose the order in which the five transactions are processed, but cannot split a transaction. The council also wants to know whether it can survive if the $180 fundraiser is delayed until next month.
1. Find an order of the five transactions that avoids the $35 overdraft fee. Show the running balance after each step and the final balance.
Read the worked answer
One safe order is fundraiser, bus, supplies, printing, donation.
| Step | Transaction | Balance |
|---|---|---|
| Start | - | $245 |
| 1 | +$180 fundraiser | $425 |
| 2 | −$140 bus | $285 |
| 3 | −$95 supplies | $190 |
| 4 | −$75 printing | $115 |
| 5 | +$60 donation | $175 |
No step ends below $0, so no fee is charged. The final balance is $175. This matches the net change: 180 − 95 − 140 − 75 + 60 = −70, and 245 − 70 = 175.
2. The treasurer instead processes the transactions in this order: supplies, bus, printing, donation, fundraiser. Track the balance and any fees. How much does this order cost compared with the safe order?
Read the worked answer
Start $245.
- Supplies: 245 − 95 = $150.
- Bus: 150 − 140 = $10.
- Printing: 10 − 75 = −$65. This transaction ends negative, so a $35 fee is charged: −65 − 35 = −$100.
- Donation: −100 + 60 = −$40. This transaction also ends negative, so another $35 fee is charged: −40 − 35 = −$75.
- Fundraiser: −75 + 180 = $105.
Total fees = $70. Final balance = $105, compared with $175 in the safe order. The bad order costs $70, exactly two overdraft fees.
3. If the $180 fundraiser is delayed, can the remaining four transactions be ordered to avoid any overdraft fee? Explain using the final balance.
Read the worked answer
The remaining four transactions have net change −95 − 140 − 75 + 60 = −$250. Starting from $245, the final balance is 245 − 250 = −$5. Since the final balance is negative, at least one transaction must end with a negative balance - at the latest, the last one. No ordering can avoid a fee. The council needs at least $5 more before all four are processed, or it must delay one of the payments.