Question

A firm offers terms of 2/20, net 50. a. What effective annual interest rate does the firm earn when a customer does not take the discount? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What effective annual interest rate does the firm earn if the discount is changed to 3 percent? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) c. What effective annual interest rate does the firm earn if the credit period is increased to 70 days? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) d. What effective annual interest rate does the firm earn if the discount period is increased to 25 days? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Effective annual interest rate b. Effective annual interest rate C. Effective annual interest rate d. Effective annual interest rate

Answer 1

a) Effective annual interest rate does the firmearn when a customer does not take the discount

Interest rate = 0.02 /0.98 = 0.0204 or 2.04%

and the interest for = 50 -20 = 30 days

Effective annual rate = ( 1 + r ) m  -1

= ( 1 + 0.0204) ( 365 / 30)  -1

= 1.0204(12.1666)  -1

= 1.2785 - 1

= 0.2785

= 27.85 %

b) interest rate = 0.03 / 0.97 = 0.03092

Effective annual rate = ( 1 + 0.03092) (365 / 30) - 1

= 1.0309212.166 -1

= 1.4484 - 1

=0.4484

=44.84 %

c ) 2 /20 net 70

interest rate = 0.02 / 0.98 = 0.0204 , 2.04%

  interest is for 50 days (70 -20)

Effective annual rate = ( 1 + 0.0204)365 / 50 - 1

= 1.02047.3 - 1

   = 1.1588 - 1

= 0.1588

= 15.88 %

d ) 2 / 25 net 50

interest rate for 25 days ( 50 - 25)

Effective annual rate = ( 1 + 0.0204) ( 365 / 25) - 1

= 1.0204 14.6 - 1

= 1.3529 - 1

= 0.3429

= 34.29%