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
To calculate the amount of discount that was charged, we can use the formula:
Discount = Face Value * Discount Rate * (Discount Days / Total Days)
a) Let's substitute the given values into the formula:
Discount = Face Value * 0.055 * (15 / 60)
We know that the proceeds received were $997.77. Therefore, we can set up the following equation:
Face Value - Discount = $997.77
We can combine the two equations and solve for the Face Value:
Face Value - (Face Value * 0.055 * (15 / 60)) = $997.77
Face Value - (Face Value * 0.01375) = $997.77
Face Value * (1 - 0.01375) = $997.77
0.98625 * Face Value = $997.77
Face Value = $997.77 / 0.98625
Face Value ≈ $1,011.54
b) To find the discount date, we need to subtract the discount days from the maturity date:
Maturity Date - Discount Days = Discount Date
In this case, the maturity date is given as 26 October 1991, and the discount days are 15 days. Let's subtract these values to find the discount date:
26 October 1991 - 15 days = 11 October 1991
Therefore, the discount date is 11 October 1991.
c) The Face Value of the note is approximately $1,011.54.
To solve this problem, we need to break it down step by step. Let's go through each part:
a) To find the amount of discount that was charged, we need to subtract the proceeds received from the face value of the note. We can use the formula:
Discount = Face Value - Proceeds Received
From the given information, we know that the proceeds received were $997.77. However, we still need to find the face value of the note. Let's move on to part c to find that value.
c) To find the face value, we can use the formula for the present value of a note:
Present Value = Future Value / (1 + (discount rate * time))
From the given information, we know that the discount rate is 5.5% and the time is 15 days. We can substitute these values into the formula. Since the time is given in days, we need to convert the discount rate and time to days as well:
Discount Rate (in days) = Discount Rate / 360
Time (in days) = 15 days
Plugging in the values, we get:
Present Value = $997.77 / (1 + (0.055 * (15 / 360)))
Present Value = $988.53
Now that we have the face value, we can go back to part a to calculate the amount of discount charged:
Discount = Face Value - Proceeds Received
Discount = $988.53 - $997.77
Discount = -$9.24
The negative sign indicates that a discount was charged. Therefore, the amount of discount that was charged is $9.24.
b) To find the discount date, we need to subtract the number of days before the maturity date from the maturity date itself. The given maturity date is 26 October 1991, and the note was discounted 15 days before that.
Maturity Date - Number of Days Before = Discount Date
26 October 1991 - 15 days = 11 October 1991
Therefore, the discount date is 11 October 1991.
So the answers to the questions are:
a) The amount of discount that was charged is $9.24.
b) The discount date is 11 October 1991.
c) The face value of the note is $988.53.