The following note was discounted at 16%. Find (a) the discount period, (b) the discount, and (c) the proceeds.
Date loan was made: March 15
Face Value: $6000
Length of Loan: 75 days
Rate: 6%
Date of Discount: April 5
To calculate the answers, we first need to determine the discount period, the discount amount, and the proceeds. Let's go step by step.
(a) To find the discount period:
The discount period refers to the number of days between the date the loan was made and the date of the discount. In this case, the loan was made on March 15, and the discount occurred on April 5. To find the discount period, we subtract the loan date from the discount date:
Discount Period = Discount Date - Loan Date = April 5 - March 15
When calculating the discount period, we need to exclude the date the loan was made and include the date of the discount. In this case, if both the loan date and discount date are considered as well, the total number of days would be 22 (including both the start and end dates).
(b) To find the discount:
The discount is the amount deducted from the face value of the note. To calculate the discount, we multiply the face value by the discount rate and the discount period. The formula for discount is as follows:
Discount = Face Value * Discount Rate * (Discount Period / 360)
In this case, the face value is $6000, the discount rate is 6%, and the discount period is determined from step (a).
(c) To find the proceeds:
The proceeds are the amount received after deducting the discount from the face value. The formula for proceeds is as follows:
Proceeds = Face Value - Discount
Now, let's calculate the values:
(a) Discount Period:
Discount Date - Loan Date = April 5 - March 15 = 22 days
(b) Discount:
Discount = $6000 * 6% * (22 / 360)
(c) Proceeds:
Proceeds = $6000 - Discount
Now that we have the formulas and steps, you can substitute the values into the formulas and calculate the discount period, discount amount, and proceeds.