A 7%,6O day note was discounted at 15 days before the maturity date. If the discount rate was 5.5% and the proceeds received were $ 997,77,find
a)the amount of discount that was charged
b)the discount date if maturity date of the note is 26 october 1991
c)face value
a) 997,77= (1+0.07(60/360))
=
i cant get the answer.
a)$2.29
b)11 october 1991
c)988.53
2014 what old fizz?at least he is gone
but this is nn000
To calculate the amount of discount that was charged, we can use the formula:
Discount = Face Value * Discount Rate * (Discount Period / 360)
Given that the discount rate is 5.5%, the discount period is 15 days, and the face value is unknown, we can plug the values into the formula and solve for the discount:
Discount = Face Value * 0.055 * (15 / 360)
Discount = 2.29
So, the amount of discount that was charged is $2.29.
To find the discount date, we need to subtract the discount period (15 days) from the maturity date (26 October 1991):
Discount Date = Maturity Date - Discount Period
Discount Date = 26 October 1991 - 15 days
Discount Date = 11 October 1991
Therefore, the discount date is 11 October 1991.
To find the face value, we can rearrange the formula for the discount calculation:
Face Value = Discount / (Discount Rate * (Discount Period / 360))
Face Value = 2.29 / (0.055 * (15 / 360))
Face Value = 988.53
So, the face value of the note is $988.53.
To solve this problem, we can break it down into three parts:
a) Find the amount of discount that was charged:
To calculate the amount of discount charged, we can use the formula:
Discount = Principal * Discount Rate * Time
Given that the Principal (face value) is unknown, we can calculate it with the proceeds received and the formula above:
Principal = Proceeds / (1 - Discount Rate * Time)
Using the given values: Proceeds = $997.77, Discount Rate = 5.5%, and Time = 15/60 years (since it was discounted 15 days before maturity, and there are 60 days in a 360-day year).
Principal = $997.77 / (1 - 0.055 * (15/60))
= $997.77 / (1 - 0.01375)
= $997.77 / 0.98625
≈ $1,012.50
Now that we have the Principal, we can find the amount of discount:
Discount = Principal * Discount Rate * Time
= $1,012.50 * 0.055 * (15/60)
≈ $2.29
Therefore, the amount of discount charged is approximately $2.29.
b) Find the discount date:
The discount date is the date when the note was discounted, which is 15 days before the maturity date. Given that the maturity date is on 26 October 1991, we can subtract 15 days to find the discount date:
Discount Date = Maturity Date - 15 days
= 26 October 1991 - 15 days
= 11 October 1991
Therefore, the discount date is 11 October 1991.
c) Find the face value:
The face value is the original value of the note, which is the Principal. From part a), we calculated the Principal to be approximately $1,012.50.
Therefore, the face value of the note is approximately $1,012.50.
Final answers:
a) The amount of discount charged is approximately $2.29.
b) The discount date is 11 October 1991.
c) The face value of the note is approximately $1,012.50.