Home health signed a 90,000 note at 11 1/2% simple interest for 180 days for electronic equipment, on October 1. On February 18, the note was sold to another firm at a discount rate of 12 1/2%. Find a) the discount period, b) the discount, and c) the proceeds.

a)

To find the discount period, we need to calculate the number of days from the date the note was sold (February 18) until the maturity date (180 days after October 1).

First, let's find the maturity date:
October has 31 days
31 - 1 = 30 days remaining in October
180 - 30 = 150 days left

Now, we know that there are 150 days left after October.

November has 30 days
December has 31 days
January has 31 days
February has 28 days (assuming it's not a leap year)

150 - 30 (November) - 31 (December) - 31 (January) = 58 days left

Now let's find the discount period, which is the difference between February 18 and the maturity date:

28 (February) - 18 = 10 days remaining in February
58 - 10 = 48 days

So, the discount period is 48 days.

b)
To calculate the discount, we'll use the formula:

Discount = (Original amount * Discount rate * Discount period) / 360 days

Discount = ($90,000 * 12.5% * 48 days) / 360 days

First, convert the discount rate into a decimal by dividing 12.5 by 100:

12.5 / 100 = 0.125

Now, plug in the values:

Discount = ($90,000 * 0.125 * 48) / 360
Discount = $5400

c)
To find the proceeds, subtract the discount from the original amount:

Proceeds = Original amount - Discount
Proceeds = $90,000 - $5,400
Proceeds = $84,600

The proceeds are $84,600.

To solve this problem, we will break it down step-by-step.

Step 1: Calculate the discount period.
The discount period is the time between the date the note was sold (February 18) and the maturity date of the note (180 days after October 1). To find the discount period, we need to determine the number of days between these two dates.

Date of Sale: February 18
Date of Note: October 1

To determine the number of days between these two dates, we can use the following formula:
Number of days = 31 (Oct) + 30 (Nov) + 31 (Dec) + 31 (Jan) + 18 (Feb)

Number of days = 141 days

Therefore, the discount period is 141 days.

Step 2: Calculate the discount.
The discount can be calculated using the formula:

Discount = Face Value of Note * Discount Rate * Discount Period

Given:
Face Value of Note = $90,000
Discount Rate = 12 1/2% = 0.125
Discount Period = 141 days

Discount = $90,000 * 0.125 * (141/360)

Discount ≈ $3,281.25

Therefore, the discount is approximately $3,281.25.

Step 3: Calculate the proceeds.
The proceeds are calculated by subtracting the discount from the face value of the note.

Proceeds = Face Value of Note - Discount

Given:
Face Value of Note = $90,000
Discount = $3,281.25

Proceeds = $90,000 - $3,281.25

Proceeds ≈ $86,718.75

Therefore, the proceeds are approximately $86,718.75.

To summarize:
a) The discount period is 141 days.
b) The discount is approximately $3,281.25.
c) The proceeds are approximately $86,718.75.

To find the discount period, we need to calculate the number of days between the sale date (February 18) and the note's original signing date (October 1).

Step 1: Find the number of days in October, November, December, January, and up to February 18.

October: 31 days
November: 30 days
December: 31 days
January: 31 days
February (up to the 18th): 18 days

Step 2: Add up the number of days in each month:

31 + 30 + 31 + 31 + 18 = 141 days

Thus, the discount period is 141 days.

Now, let's move on to finding the discount. The discount is calculated using the discount rate and the face value of the note. The face value of the note is $90,000.

Step 3: Calculate the discount rate as a decimal:

12 1/2% = 12.5%

12.5% = 12.5/100 = 0.125

Step 4: Calculate the discount amount:

Discount = Discount Rate * Face Value of the Note

Discount = 0.125 * $90,000 = $11,250

Therefore, the discount is $11,250.

Finally, we can find the proceeds, which is the amount received when the note is sold after deducting the discount from the face value.

Step 5: Calculate the proceeds:

Proceeds = Face Value of the Note - Discount

Proceeds = $90,000 - $11,250 = $78,750

Hence, the proceeds are $78,750.

To summarize:
a) The discount period is 141 days.
b) The discount is $11,250.
c) The proceeds are $78,750.