How is the percentage cost of an early settlement discount calculated?

How is the percentage cost of an early settlement discount calculated?

• A. ([100/100-d]^(365/t)) - 1
• B. [(100-d)/(100)]^(t/365) - 1
• C. [(100+d)/(100)]^(365/t) - 1
• D. [100 x (1 - d)]^(t/365) - 1

Answer: (A)

The calculation of the percentage cost of an early settlement discount is based on understanding how discounts are applied and the financial implications of settling earlier than the due date. The correct formula is derived from the relationship between the discount rate, the period of credit, and the time value of money. The first choice provides the correct formula: \(([100/100-d]^{(365/t)}) - 1\). This formula establishes a connection between the discount given (d) and the amount that would be required to pay if the discount isn't taken. Essentially, it tells us how much more one pays if they opt not to take the discount and instead pay the full amount later. Breaking this down, the denominator, \(100 - d\), represents the remaining amount after the discount is applied, while \(100\) is the original amount. When divided, \(100/100-d\) shows how much more needs to be paid relative to the amount after the discount. Raising this fraction to the power of \(365/t\) effectively annualizes the cost of the discount, enabling comparisons over different credit terms or periods. This calculation is key for businesses that offer discounts for early payment, as it aids in understanding the real cost of not taking that discount

The calculation of the percentage cost of an early settlement discount is based on understanding how discounts are applied and the financial implications of settling earlier than the due date. The correct formula is derived from the relationship between the discount rate, the period of credit, and the time value of money.

The first choice provides the correct formula: (([100/100-d]^{(365/t)}) - 1). This formula establishes a connection between the discount given (d) and the amount that would be required to pay if the discount isn't taken. Essentially, it tells us how much more one pays if they opt not to take the discount and instead pay the full amount later.

Breaking this down, the denominator, (100 - d), represents the remaining amount after the discount is applied, while (100) is the original amount. When divided, (100/100-d) shows how much more needs to be paid relative to the amount after the discount. Raising this fraction to the power of (365/t) effectively annualizes the cost of the discount, enabling comparisons over different credit terms or periods.

This calculation is key for businesses that offer discounts for early payment, as it aids in understanding the real cost of not taking that discount