Chapter 7, Problem 7.11P

To determine

Note receivable:

Note receivable refers to a written promise for the amounts to be received within a stipulated period of time. This written promise is issued by a debtor or borrower to lender or creditor. Notes receivable is an asset of a business.

To determine: The amount of cash received from the discounting of the following notes:

Answer to Problem 7.11P

Note	Note Face Value	Date of Note	Interest Rate	Date Discounted	Discount Rate	Proceeds Received
1	$50,000	3/31/2016	8%	6/30/2016	10%	$50,350 (Note1)
2	50,000	3/31/2016	8%	9/30/2016	10%	51,675 (Note 2)
3	50,000	3/31/2016	8%	9/30/2016	12%	51,410 (Note 3)
4	80,000	6/30/2016	6%	10/31/2016	10%	81,027 (Note 4)
5	80,000	6/30/2016	6%	10/31/2016	12%	80,752 (Note 5)
6	80,000	6/30/2016	6%	11/30/2016	10%	81,713 (N ote 6)

Table (1)

Explanation of Solution

Note 1:

Compute the amount of cash proceeds:

$\begin{array}{c}\text{Cash Proceeds = Maturity Value}-\text{Discount}\\ \text{=}\text{\$53,000(2)}-\text{\$2,650}\text{(3)}\\ \text{=}\text{\$50,350}\end{array}$

Working notes:

Compute the amount of interest on maturity:

Principal = $50,000

Rate of interest = 8%

Period = 9 Months (March 31, 2016 to December 31 2016)

$\begin{array}{c}\text{Interest = Principal }\times \text{ Rate of interest }\times \text{ Interest period}\\ \text{ = \$50,000}\times \frac{8}{100}\times \frac{9}{12}\\ =\$3,000\end{array}$ (1)

Compute the maturity value:

$\begin{array}{c}\text{Maturity Value = Face value + Interest}\\ \text{= \$50,000 + \$3,000}\\ \text{=}\text{\$53,000}\end{array}$ (2)

Compute the amount discount on discounting the note:

$\begin{array}{c}\text{Discount = Maturity Value }\times \text{ Rate of interest }\times \text{ Remaining period}\\ \text{ = \$53,000}\times \frac{10}{100}\times \frac{6\left[9\left(\text{Total Period}\right)-3\left(\text{Issue date to Discount Date}\right)\right]}{12}\\ =\$2,650\end{array}$ (3)

Note 2:

Compute the amount of cash proceeds:

$\begin{array}{c}\text{Cash Proceeds = Maturity Value }-\text{ Discount}\\ \text{=}\text{\$53,000 (4)}-\$1,325\text{(6)}\\ =\$51,675\end{array}$

Working notes:

Compute the amount of interest on maturity:

Principal = $50,000

Rate of interest = 8%

Period = 9 Months (March 31 to December 31)

$\begin{array}{c}\text{Interest = Principal }\times \text{ Rate of interest }\times \text{ Interest period}\\ \text{ = \$50,000}\times \frac{8}{100}\times \frac{9}{12}\\ =\$3,000\end{array}$ (4)

Compute the maturity value:

$\begin{array}{c}\text{Maturity Value = Face value + Interest}\\ \text{= \$50,000 + \$3,000}\\ \text{=}\text{\$53,000}\end{array}$ (5)

Compute the amount discount on discounting the note:

$\begin{array}{c}\text{Discount = Maturity Value }\times \text{ Rate of interest }\times \text{ Remaining period}\\ \text{ = \$53,000}\times \frac{10}{100}\times \frac{3\left[9\left(\text{Total Period}\right)-6\left(\text{Issue date to Discount Date}\right)\right]}{12}\\ =\$1,325\end{array}$ (6)

Note 3:

Compute the amount of cash proceeds:

$\begin{array}{c}\text{Cash Proceeds = Maturity Value }-\text{ Discount}\\ \text{=}\text{\$53,000 (8)}-\$1,590\text{(9)}\\ =\$51,410\end{array}$

Working notes:

Compute the amount of interest on maturity:

Principal = $50,000

Rate of interest = 8%

Period = 9 Months (March 31 to December 31)

$\begin{array}{c}\text{Interest = Principal }\times \text{ Rate of interest }\times \text{ Interest period}\\ \text{ = \$50,000}\times \frac{8}{100}\times \frac{9}{12}\\ =\$3,000\end{array}$ (7)

Compute the maturity value:

$\begin{array}{c}\text{Maturity Value = Face value + Interest}\\ \text{= \$50,000 + \$3,000}\\ \text{=}\text{\$53,000}\end{array}$ (8)

Compute the amount discount on discounting the note:

$\begin{array}{c}\text{Discount = Maturity Value }\times \text{ Rate of interest }\times \text{ Remaining period}\\ \text{ = \$53,000}\times \frac{12}{100}\times \frac{3\left[9\left(\text{Total Period}\right)-6\left(\text{Issue date to Discount Date}\right)\right]}{12}\\ =\$1,590\end{array}$ (9)

Note 4:

Compute the amount of cash proceeds:

$\begin{array}{c}\text{Cash Proceeds = Maturity Value }-\text{ Discount}\\ \text{=}\text{\$82,400 (11)}-\$1,373\text{(12)}\\ =\$81,027\end{array}$

Working notes:

Compute the amount of interest on maturity:

Principal = $80,000

Rate of interest = 6%

Period = 6 Months (June 30 to December 31)

$\begin{array}{c}\text{Interest = Principal }\times \text{ Rate of interest }\times \text{ Interest period}\\ \text{ = \$80,000}\times \frac{6}{100}\times \frac{6}{12}\\ =\$2,400\end{array}$ (10)

Compute the maturity value:

$\begin{array}{c}\text{Maturity Value = Face value + Interest}\\ \text{= \$80,000 + \$2,400}\\ \text{=}\text{\$82,400}\end{array}$ (11)

Compute the amount discount on discounting the note:

  $\begin{array}{c}\text{Discount = Maturity Value }\times \text{ Rate of interest }\times \text{ Remaining period}\\ \text{ = \$82,400}\times \frac{10}{100}\times \frac{2\left[6\left(\text{Total Period}\right)-4\left(\text{Issue date to Discount Date}\right)\right]}{12}\\ =\$1,373\end{array}$ (12)

Note 5:

Compute the amount of cash proceeds:

$\begin{array}{c}\text{Cash Proceeds = Maturity Value }-\text{ Discount}\\ \text{=}\text{\$82,400 (14)}-\text{\$1,648}\text{(15)}\\ =\$80,752\end{array}$

Working notes:

Compute the amount of interest on maturity:

Principal = $80,000

Rate of interest = 6%

Period = 6 Months (June 30 to December 31)

$\begin{array}{c}\text{Interest = Principal }\times \text{ Rate of interest }\times \text{ Interest period}\\ \text{ = \$80,000}\times \frac{6}{100}\times \frac{6}{12}\\ =\$2,400\end{array}$ (13)

Compute the maturity value:

$\begin{array}{c}\text{Maturity Value = Face value + Interest}\\ \text{= \$80,000 + \$2,400}\\ \text{=}\text{\$82,400}\end{array}$ (14)

Compute the amount discount on discounting the note:

$\begin{array}{c}\text{Discount = Maturity Value }\times \text{ Rate of interest }\times \text{ Remaining period}\\ \text{ = \$82,400}\times \frac{12}{100}\times \frac{2\left[6\left(\text{Total Period}\right)-4\left(\text{Issue date to Discount Date}\right)\right]}{12}\\ =\$1,648\end{array}$ (15)

Note 6:

Compute the amount of cash proceeds:

$\begin{array}{c}\text{Cash Proceeds = Maturity Value }-\text{ Discount}\\ \text{=}\text{\$82,400 (17)}-\text{\$687 (18)}\\ =\$81,713\end{array}$

Working notes:

Compute the amount of interest on maturity:

Principal = $80,000

Rate of interest = 6%

Period = 6 Months (June 30 to December 31)

$\begin{array}{c}\text{Interest = Principal }\times \text{ Rate of interest }\times \text{ Interest period}\\ \text{ = \$80,000}\times \frac{6}{100}\times \frac{6}{12}\\ =\$2,400\end{array}$ (16)

Compute the maturity value:

$\begin{array}{c}\text{Maturity Value = Face value + Interest}\\ \text{= \$80,000 + \$2,400}\\ \text{=}\text{\$82,400}\end{array}$ (17)

Compute the amount discount on discounting the note:

$\begin{array}{c}\text{Discount = Maturity Value }\times \text{ Rate of interest }\times \text{ Remaining period}\\ \text{ = \$82,400}\times \frac{10}{100}\times \frac{1\left[6\left(\text{Total Period}\right)-5\left(\text{Issue date to Discount Date}\right)\right]}{12}\\ =\$687\end{array}$ (18)