An invoice for $14,408 dated September 27 with terms of 4/20, 2/35, n/40 was partially paid on October 3. If the invoice balance was reduced to $8,003, what was the amount of the payment? Assume the payment was received on the date indicated.

For full marks your answer(s) should be rounded to the nearest cent.

To solve this problem, we first need to understand the payment terms of the invoice:

- **4/20** means a 4% discount is available if payment is made within 20 days.
- **2/35** means a 2% discount is available if payment is made within 35 days.
- **n/40** means the net amount (full invoice amount without discount) is due within 40 days.

### Step-by-Step Calculation:

1. **Invoice Details**:
   - Invoice amount: **$14,408**
   - Invoice date: **September 27**
   - Payment date: **October 3**

2. **Determine the Discount Period**:
   - The payment date of October 3 is within 6 days after the invoice date (September 27 to October 3 is 6 days).
   - Since 6 days is within the 20-day period, the **4% discount** applies.

3. **Calculate the Amount Paid with Discount**:
   - Let $ P $ be the amount of the payment made on October 3.
   - The discount applied on the payment made is 4%.

   Since the invoice balance after the payment is reduced to $8,003, this means:

   \[
   \text{Remaining balance} = \text{Original invoice amount} - \text{Discounted payment}
   \]

   Let’s calculate the discounted payment first.

4. **Calculate the Discounted Payment**:
   - Let $ X $ be the amount of the payment before applying the discount.
   - The payment amount $ P $ is after applying the 4% discount:

   \[
   P = X - (0.04 \times X) = X \times (1 - 0.04) = X \times 0.96
   \]

   Given that after this payment, the balance is reduced to $8,003, we can calculate $ X $ as:

   \[
   \text{New balance} = \text{Original amount} - \text{Discounted payment}
   \]

   \[
   8,003 = 14,408 - 0.96X
   \]

   Solving for $ X $:

   \[
   0.96X = 14,408 - 8,003
   \]

   \[
   0.96X = 6,405
   \]

   \[
   X = \frac{6,405}{0.96}
   \]

   \[
   X = 6,673.9583
   \]

   Therefore, $ X \approx 6,673.96 $.

5. **Calculate the Amount Paid (P)**:

   \[
   P = 0.96 \times 6,673.96 = 6,406.6016
   \]

   \[
   P \approx 6,406.60
   \]

Thus, the amount of the payment made on October 3 was **$6,406.60**.

### Conclusion:
The payment amount made on October 3, applying the 4% discount, is **$6,406.60**.

Would you like any further details or have any questions?

Here are 5 additional related questions:
1. What would have been the payment amount if it was made after 20 days but before 35 days?
2. How much discount was availed due to the early payment on October 3?
3. What is the effective discount percentage if the payment is made exactly on the last discount day?
4. How would the payment calculation change if the invoice terms were 5/10, 3/20, n/30?
5. What is the remaining balance if no discount was applied to a partial payment of $6,000?

**Tip:** When working with discount terms, always check which discount applies based on the payment date relative to the invoice date.

Learn how to calculate partial payments and discounts on an invoice using finance principles. Solve a specific problem involving an invoice for $14,408 with terms of 4/20, 2/35, n/40, partially paid on October 3, reducing the balance to $8,003. Includes step-by-step calculations and detailed explanations.

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