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

Answer:

case 1: 12.49%

case 2: 21.20%

case 3:   9.48%

case 4:  13.98%

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%