16. A 7%, 60-day note was discounted 15 days before the maturity date. If the discount rate was 5.59% and the proceeds received were RM997.77, find:
(a) the amount of discount that was charged
(b) the discount date if the maturity date of the note is 26 October 2021
(c) the face value of the note
(a) To find the amount of discount that was charged, we can use the formula:
Discount = Face Value × Discount Rate × Time
Given that the discount rate is 5.59% and the time is 15 days, we need to convert the time to a fraction of a year. Since there are 365 days in a year, the fraction of a year is:
Time = 15/365
Now we can calculate the discount:
Discount = Face Value × 0.0559 × (15/365)
Since the proceeds received were RM997.77, we can write the equation:
Face Value - Discount = RM997.77
Solving for the discount, we have:
Discount = Face Value - RM997.77
Plugging in the value of the discount from the first equation, we get:
Face Value × 0.0559 × (15/365) = Face Value - RM997.77
Simplifying the equation gives:
0.0559 × (15/365) = 1 - 997.77/Face Value
Let's solve for the Face Value now. Multiplying both sides of the equation by Face Value gives:
(0.0559 × 15 × Face Value) / 365 = Face Value - RM997.77
Expanding the left side of the equation gives:
0.0559 × 15 = 365 × Face Value - 365 × RM997.77
Simplifying further gives:
0.8385 = 365 × Face Value - 365 × RM997.77
Rearranging the equation gives:
365 × Face Value = 365 × RM997.77 + 0.8385
Dividing both sides by 365 gives:
Face Value = (365 × RM997.77 + 0.8385) / 365
Calculating the value of Face Value will give the result for part (c).
(b) To find the discount date, we subtract the discount period from the maturity date.
Discount Period = Maturity Date - Discount Date
Given that the maturity date is 26 October 2021 and the note was discounted 15 days before the maturity date, we have:
Discount Period = 26 October 2021 - 15 days
Calculating the result will give the discount date for part (b).