1. A 120-day simple discount promissory note for $12,000 with a simple discount rate of 9% was signed on July 14. It was discounted on August 30 at 9.5%. Find the proceeds at the time of the sale.
2. 8. A $15,000 T-bill is purchased at a 3.85% discount rate for 16 weeks. Find (a) the purchase price of the T-bill, (b) the maturity value, (c) the interest earned, (d) the effective rate of interest to the nearest hundredth of a percent.
ooh a hard one...2012 we are in 2018!!!thats why theres noone here.this is a OLD SITE oooohhhh...
A 120-day simple discount promissory note for $12,000 with a simple discount rate of 9% was signed on July 14. It was discounted on August 30 at 9.5%. Find the proceeds at the time of the sale.
1. To find the proceeds at the time of the sale, we need to calculate the discount and deduct it from the face value of the promissory note.
Step 1: Calculate the discount for the 120-day promissory note.
Discount = Face Value * Discount Rate * Time
Discount = $12,000 * 9% * (120/360) [Since the note was discounted on August 30, which is 46 days after July 14, we divide by 360 since it is a 360-day year.]
Discount = $360
Step 2: Calculate the proceeds at the time of the sale.
Proceeds = Face Value - Discount
Proceeds = $12,000 - $360
Proceeds = $11,640
Therefore, the proceeds at the time of the sale for the promissory note is $11,640.
2. Let's find the information requested regarding the T-bill:
Step 1: Calculate the purchase price of the T-bill.
Purchase Price = Face Value * (1 - Discount Rate)
Purchase Price = $15,000 * (1 - 3.85%)
Purchase Price = $15,000 * (1 - 0.0385)
Purchase Price = $15,000 * (0.9615)
Purchase Price = $14,423.75
(a) The purchase price of the T-bill is $14,423.75.
Step 2: Calculate the maturity value.
Maturity Value = Face Value + Interest Earned
Maturity Value = $15,000 + $14,423.75 * (3.85% * (16/52))
Maturity Value = $15,000 + $697.50
(b) The maturity value of the T-bill is $15,697.50.
Step 3: Calculate the interest earned.
Interest Earned = Maturity Value - Purchase Price
Interest Earned = $15,697.50 - $14,423.75
(c) The interest earned on the T-bill is $1,273.75.
Step 4: Calculate the effective rate of interest.
Effective Rate of Interest = (Interest Earned / Purchase Price) * 100
Effective Rate of Interest = ($1,273.75 / $14,423.75) * 100
(d) The effective rate of interest, rounded to the nearest hundredth of a percent, is 8.82%.
To solve both of these problems, you will need to use the formula for simple discount:
Discount = Principal * Rate * Time
The proceeds at the time of the sale can then be calculated using the formula:
Proceeds = Principal - Discount
For the first problem:
1. Calculate the discount for the first rate on August 30:
Discount = $12,000 * 0.095 * (30 days / 360 days)
Discount = $95
2. Calculate the discount for the second rate from July 14 to August 30:
Discount = $12,000 * 0.09 * (47 days / 360 days)
Discount = $564
3. Calculate the total discount:
Total Discount = $95 + $564
Total Discount = $659
4. Calculate the proceeds at the time of sale:
Proceeds = $12,000 - $659
Proceeds = $11,341
The proceeds at the time of sale for the 120-day simple discount promissory note are $11,341.
For the second problem:
(a) The purchase price of the T-bill:
Purchase Price = Maturity Value - Discount
To find the purchase price, we need to use the formula for discount:
Discount = Principal * Rate * Time
For this problem, the discount is not given. But we know the discount rate and the time period.
Discount = $15,000 * 0.0385 * (16 weeks / 52 weeks)
Discount = $714.23
Hence,
Purchase Price = $15,000 - $714.23
(b) The maturity value:
The maturity value is the face value of the T-bill, which is $15,000.
(c) The interest earned:
Interest Earned = Maturity Value - Purchase Price
(d) The effective rate of interest:
To find the effective rate of interest, we can use the formula:
Effective Rate = (Interest Earned / Purchase Price) * (365 / Time)
Plug in the values to get the effective rate of interest.
These steps should help you find the answers to problem 2.