Chapter 20, Problem 5QP

Terms of Sale [LO1] A firm offers terms of 1/10, net 30. What effective annual interest rate does the firm earn when a customer does not take the discount? Without doing any calculations, explain what will happen to this effective rate if:

a. The discount is changed to 2 percent.

b. The credit period is increased to 45 days.

c. The discount period is increased to 15 days.

Summary Introduction

To determine: The effective annual rate (EAR)

Introduction:

Credit term refers to customer’s ability to acquire goods before making payment, depends on the trust that payment will be paid in future.

Answer to Problem 5QP

The effective annual rate (EAR) is 20.13%.

Explanation of Solution

Given information:

The terms “1/10 net 30” means the customers receive 1% discount if they make the payment in 10 days, with the total amount due in 30 days if the discount is not received.

In this case, 30 days is the credit period, 10 days is the period of discount, and 2% is the amount of cash discount.

Here, the percentage of discount interest is 1% on $30-10=20$ days’ credit.

The formula to calculate the periods per year:

$\begin{array}{c}\text{Periods per year = }\frac{\text{Number of days in a year}}{\text{Days}\text{in}\text{period}}\\ \text{= }\frac{\text{365}}{\text{20}}\\ \text{=18}\text{.25 }\end{array}$

Hence, the periods per year is 18.25.

The formula to calculate the periodic interest rate:

$\begin{array}{c}\text{Periodic interest rate = }\frac{\text{Discount}\text{rate}}{1-\text{Discount}\text{rate}}\\ \text{= }\frac{\text{0}\text{.010}}{\left(1-\text{0}\text{.010}\right)}\\ \text{=}\frac{0.01}{0.09}\\ \text{=0}\text{.0101 or 1}\text{.01\%}\end{array}$

Hence, the periodic interest rate is 1.01%.

The formula to calculate effective annual rate:

$\begin{array}{c}{\text{Effective annual rate (EAR) = 1+Periodic interest rate}}^{\text{m}}-\text{1}\\ \text{=1+0}{\text{.0101}}^{18.25}-1\\ ={1.0101}^{18.25}-1\\ =0.2013\text{or}20.13\%\end{array}$

Hence, the effective interest rate is 20.13%.

Summary Introduction

To determine: The EAR.

Answer to Problem 5QP

The effective annual rate (EAR) is 44.59%.

Explanation of Solution

Given information:

The terms “2/10 net 30” means the customers receive 2% discount if they make the payment in 10 days, with the total amount due in 30 days if the discount is not received.

In this case, 30 days is the credit period, 10 days is the period of discount, and 2% is the amount of cash discount.

Here, the percentage of discount interest is 2% on $30-10=20$ days’ credit.

The formula to calculate the periods per year:

$\begin{array}{c}\text{Periods per year = }\frac{\text{Number of days in a year}}{\text{Days}\text{in}\text{period}}\\ \text{= }\frac{\text{365}}{\text{20}}\\ \text{=18}\text{.25 }\end{array}$

Hence, the periods per year is 18.25.

The formula to calculate the periodic interest rate:

$\begin{array}{c}\text{Periodic interest rate = }\frac{\text{Discount}\text{rate}}{1-\text{Discount}\text{rate}}\\ \text{= }\frac{\text{0}\text{.02}}{\left(1-\text{0}\text{.2}\right)}\\ \text{=}\frac{0.02}{0.98}\\ \text{=0}\text{.0204 or 2}\text{.04\%}\end{array}$

Hence, the periodic interest rate is 2.04%.

The formula to calculate effective annual rate:

$\begin{array}{c}{\text{Effective annual rate (EAR) = 1+Periodic interest rate}}^{\text{m}}-\text{1}\\ \text{=1+0}{\text{.0204}}^{18.25}-1\\ ={1.0204}^{18.25}-1\\ =0.4459\text{or}44.59\%\end{array}$

Hence, the effective interest rate is 44.59%.

Summary Introduction

To determine: The effective annual rate (EAR)

Answer to Problem 5QP

The effective annual rate (EAR) is 11.05%.

Explanation of Solution

Given information:

The terms “1/10 net 45” means the customers receive a 1% discount if they pay in 10 days, with the total amount due in 45 days if the discount is not received.

In this case, 45 days is the credit period, 10 days is the period of discount, and 1% is the amount of cash discount.

Here, the percentage of discount interest is 1% on $45-10=35$ days’ credit.

The formula to calculate the periods per year:

$\begin{array}{c}\text{Periods per year = }\frac{\text{Number of days in a year}}{\text{Days}\text{in}\text{period}}\\ \text{= }\frac{\text{365}}{35}\\ \text{=10}\text{.43 }\end{array}$

Hence, the periods per year is 10.43.

The formula to calculate the periodic interest rate:

$\begin{array}{c}\text{Periodic interest rate = }\frac{\text{Discount}\text{rate}}{1-\text{Discount}\text{rate}}\\ \text{= }\frac{\text{0}\text{.010}}{\left(1-\text{0}\text{.010}\right)}\\ \text{=}\frac{0.01}{0.09}\\ \text{=0}\text{.0101 or 1}\text{.01\%}\end{array}$

Hence, the periodic interest rate is 1.01%.

The formula to calculate effective annual rate:

$\begin{array}{c}{\text{Effective annual rate (EAR) = 1+Periodic interest rate}}^{\text{m}}-\text{1}\\ \text{=1+0}{\text{.0101}}^{10.43}-1\\ ={1.0101}^{10.43}-1\\ =0.1105\text{or}11.05\%\end{array}$

Hence, the effective interest rate is 11.05%.

Summary Introduction

To determine: The effective annual rate (EAR)

Answer to Problem 5QP

The effective annual rate (EAR) is 27.71%.

Explanation of Solution

Given information:

The terms “1/15 net 30” mean the customers receive a 1% discount if they pay in 10 days, with the total amount due in 30 days if the discount is not received.

In this case, 30 days is the credit period, 15 days is the period of discount, and 2% is the amount of cash discount.

Here, the percentage of discount interest is 1% on $30-15=15$ days’ credit.

The formula to calculate the periods per year:

$\begin{array}{c}\text{Periods per year = }\frac{\text{Number of days in a year}}{\text{Days}\text{in}\text{period}}\\ \text{= }\frac{\text{365}}{15}\\ \text{=24}\text{.33 }\end{array}$

Hence, the periods per year is 24.33.

The formula to calculate the periodic interest rate:

$\begin{array}{c}\text{Periodic interest rate = }\frac{\text{Discount}\text{rate}}{1-\text{Discount}\text{rate}}\\ \text{= }\frac{\text{0}\text{.010}}{\left(1-\text{0}\text{.010}\right)}\\ \text{=}\frac{0.01}{0.09}\\ \text{=0}\text{.0101 or 1}\text{.01\%}\end{array}$

Hence, the periodic interest rate is 1.01%.

The formula to calculate effective annual rate:

$\begin{array}{c}{\text{Effective annual rate (EAR) = 1+Periodic interest rate}}^{\text{m}}-\text{1}\\ \text{=1+0}{\text{.0101}}^{24.33}-1\\ ={1.0101}^{24.33}-1\\ =0.2771\text{or}27.71\%\end{array}$

Hence, the effective interest rate is 27.71%.