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.

Answer 1

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.