A 7%, 60-day note was discounted 15 days before the maturity date. If the discount rate was 5.5% and the proceeds received were RM997.77, calculate:
the amount of discount that was charged
the discount date if the maturity date of the note is 26 October 2018, and
the face value of the note.
1. First, let's find the amount of discount that was charged.
We know that the bank's proceeds were RM997.77 and the discount rate was 5.5%. Let D represent the amount of the discount.
Bank's proceeds = face value of the note (FV) - discount (D)
997.77 = FV - D
From the information given, we know that the note was discounted for 45 days (60-day note discounted 15 days before maturity). The discount rate of 5.5% is annual, so let's convert it to a daily rate:
Daily discount rate = annual discount rate / 360 = 5.5% / 360 = 0.015278, and we need it in percentage so 0.015278*100 = 1.5278%
Now, we can apply the formula for calculating the discount:
D = (face value of the note * daily discount rate * number of days discounted) / 100
D = (FV * 1.5278% * 45) / 100
Since the bank's proceeds are the difference between the face value and the discount, we have:
997.77 = FV - D
997.77 = FV - (FV * 1.5278% * 45) / 100
To solve for FV, we can first simplify the equation:
997.77 = FV - (1.5278% * 45 * FV) / 100
997.77 = FV(1 - (1.5278% * 45) / 100)
Now let's solve for FV:
FV = 997.77 / (1 - (1.5278% * 45) / 100)
FV = 997.77 / (1 - 0.68691 / 100)
FV = 997.77 / (1 - 0.0068691)
FV = 997.77 / 0.9931309
FV = 1,004.72641
Now that we have the face value of the note, let's find the amount of discount (D):
D = (1.5278% * 45 * 1,004.72641) / 100
D = 686.94821 / 100
D = 6.8694821
Therefore, the amount of discount that was charged is RM6.87 (approximately).
2. To find the discount date, we know that the maturity date is 26 October 2018, and the note was discounted 15 days before the maturity date. So, we subtract 15 days from the maturity date:
Discount date = 26 October 2018 - 15 days
Discount date = 11 October 2018
3. The face value of the note is approximately RM1,004.73.