Hoyes Lumber generally receives three checks per month. A check for $10,560 clears in 2 days, a check for $6,300 clears in 4 days, and a check for $7,570 clears in 3 days. Assuming 30 days in each month, what is the average daily float?

Question

BlackTom AI · Accepted Answer

Average daily float equals the total "dollar‑days" of checks in transit divided by the number of days in the period. A dollar‑day is the amount of money times the number of days it is unavailable.

Relevant concepts:
- Float (in dollars) is the average balance tied up due to clearning delays.
- For each item: dollar-days = check amount × clearing days.
- Average daily float over the month = (sum of dollar-days) ÷ (days in month).

Step‑by‑step calculation with all intermediate steps:
1. Compute dollar‑days for each check:
   - Check for $10,560 clearing in 2 days: 10,560 × 2 = 21,120 dollar‑days.
   - Check for $6,300 clearing in 4 days: 6,300 × 4 = 25,200 dollar‑days.
   - Check for $7,570 clearing in 3 days: 7,570 × 3 = 22,710 dollar‑days.
2. Sum the dollar‑days: 21,120 + 25,200 + 22,710 = 69,030 dollar‑days.
3. Divide by the number of days in the month (30): 69,030 ÷ 30 = 2,301.

Why this is correct:
- The dollar‑day method accounts for both the size of each check and how long each is outstanding; dividing by the period length gives the average balance unavailable each day. Thus the firm’s average daily float is $2,301.

Why common incorrect approaches fail:
- Averaging the check amounts and averaging the days and then multiplying (or dividing total amounts by 30) ignores the pairing of each amount with its specific clearing time and yields incorrect results.
- Dividing the total dollar‑days by the number of checks (instead of days) gives a meaningless per‑check dollar‑days rather than an average daily balance.

Conclusion: The calculated average daily float is $2,301.00, which matches the provided answer.

Hoyes Lumber generally receives three checks per month. A check for $10,560 clears in 2 days, a check for $6,300 clears in 4 days, and a check for $7,570 clears in 3 days. Assuming 30 days in each month, what is the average daily float?单项选择题

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