Math Problem Statement

An invoice for $10,388 dated May 20 with terms of 2/10, 1/25, n/60 was partially paid on May 27. If the invoice balance was reduced to $5,423, what was the amount of the payment? Assume the payment was received on the date indicated.

Solution

The terms of the invoice are as follows:

  • 2/10: A 2% discount is offered if the payment is made within 10 days.
  • 1/25: A 1% discount is offered if the payment is made within 25 days.
  • n/60: The net amount (no discount) is due in 60 days.

The invoice is dated May 20, and the payment was made on May 27, which is within 10 days. Therefore, the 2% discount applies to the portion of the invoice that was paid.

Step-by-Step Calculation

  1. Original invoice amount: $10,388

  2. Remaining balance after payment: $5,423

  3. Amount paid:
    Amount Paid=Original Invoice AmountRemaining Balance=10,3885,423=4,965\text{Amount Paid} = \text{Original Invoice Amount} - \text{Remaining Balance} = 10,388 - 5,423 = 4,965 The amount of the payment before applying the discount is $4,965.

  4. Discount on the payment: Since the payment is within 10 days, a 2% discount applies. To find the full value before the discount: Amount before Discount=Amount Paid1Discount Percentage=4,96510.02=4,9650.98\text{Amount before Discount} = \frac{\text{Amount Paid}}{1 - \text{Discount Percentage}} = \frac{4,965}{1 - 0.02} = \frac{4,965}{0.98}

Let's calculate this.The amount before the 2% discount was applied is approximately $5,066.33.

Therefore, the total payment made on May 27 was $5,066.33, but after applying the 2% discount, the amount effectively paid was $4,965.

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

  1. How would the payment change if it was made after the 10-day discount period but within 25 days?
  2. What would be the total interest or discount savings if the full invoice was paid within 10 days?
  3. How is the percentage discount calculated for different payment periods?
  4. How would the remaining balance be affected if no discount was applied?
  5. How does the concept of cash discounts affect business cash flow?

Tip: When applying cash discounts, always check the timing of the payment relative to the invoice terms to maximize savings.

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Math Problem Analysis

Mathematical Concepts

Percentages
Discounts
Financial Mathematics

Formulas

Amount Paid = Original Invoice Amount - Remaining Balance
Amount before Discount = Amount Paid / (1 - Discount Percentage)

Theorems

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Suitable Grade Level

Grades 9-12