Question

A firm offers terms of 1.6/10, net 60. a. What effective annual interest rate does the firm earn when a customer does not take the discount? (Use 365 days a year. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Effective annual interest rate 12.49 12.49 Correct % b. What effective annual interest rate does the firm earn if the terms are changed to 2.6/10, net 60, and the customer does not take the discount? (Use 365 days a year. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Effective annual interest rate 21.20 21.20 Correct % c. What effective annual interest rate does the firm earn if the terms are changed to 1.6/10, net 75, and the customer does not take the discount? (Use 365 days a year. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Effective annual interest rate 9.48 9.48 Correct % d. What effective annual interest rate does the firm earn if the terms are changed to 1.6/15, net 60, and the customer does not take the discount? (Use 365 days a year. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

The effective annual interest rate a firm earns when offering credit terms of 1.6/15, net 60, and the customer does not take the discount is 12.35%.

Step-by-step explanation:

Effective Annual Interest Rate Calculation

To calculate the effective annual interest rate a firm earns when a customer does not take the discount for the credit terms 1.6/15, net 60, we need to understand the cost of not taking the discount. The cost for the customer to not take the discount is essentially the interest the firm earns. The formula to calculate the effective rate (ER) is given by:

ER = (1 + Discount Rate / (1 - Discount Rate))^(365 / Payment Period) - 1

In this scenario, the discount rate is 1.6% (0.016), and the difference between the discount period and the net period is 60 - 15 = 45 days. Substituting these values into our formula:

ER = (1 + 0.016 / (1 - 0.016))^(365 / 45) - 1

Calculating the above expression:

ER = (1 + 0.016 / 0.984)^(365 / 45) - 1
ER = (1 + 0.016267)^(8.111) - 1
ER = 1.014138^(8.111) - 1
ER = 1.123456 - 1
ER = 0.123456

Convert this to a percentage:

ER = 12.35%

Therefore, if a firm changes its credit terms to 1.6/15, net 60, and the customer does not take the discount, the effective annual interest rate the firm earns is 12.35%.

Answer 2

case 1: 12.49%

case 2: 21.20%

case 3: 9.48%

case 4: 13.98%

Step-by-step explanation:

the rate stands for the period between the last day of the discount and the last day the invoice can be cancelled at nominal.

we equalize this with a rate which capitalize annually and solve for this rate:

`(1+discount)^((net-d_t)/365) =1+r_e\\ r_e = \sqrt[(net-d_t)/365]{1+discount}`

case 1:

`r_e = \sqrt[(60-10)/365]{1+0.016}`

re = 0.1249 = 12.49%

case 2:

`r_e = \sqrt[(60-10)/365]{1+0.026}`

re = 0.2120 = 21.20%

case 3:

`r_e = \sqrt[(75-10)/365]{1+0.016}`

re = 0.0948 = 9.48%

case 4:

`r_e = \sqrt[(60-15)/365]{1+0.016}`

re = 0.13977 = 13.98%