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)face vaalue
what is the formula
To solve this problem, we can use the formula for simple interest, which is:
Interest = Principal x Rate x Time
In this case, the principal is the face value of the note, the interest is the discount charged, and the rate is the discount rate. The time is the difference between the maturity date and the discount date in terms of the interest period of the note.
a) To find the amount of discount that was charged, we can use the formula:
Discount = Principal x Rate x Time
In this case, the principal is the face value of the note, the rate is 5.5%, and the time is (60 - 15) / 360 years (since it's a 60-day note), which is 45/360 or 1/8 of a year.
So, the discount can be calculated as:
Discount = Face Value x 5.5% x 1/8
b) To find the face value of the note, we can use the formula:
Face Value = Proceeds / (1 - Rate x Time)
In this case, the proceeds are given as $997.77, the rate is 5.5%, and the time is (60 - 15) / 360 years (as explained above).
So, the face value can be calculated as:
Face Value = $997.77 / (1 - 5.5% x 1/8)
Now, let's calculate the values using the formulas.