I want to know the formula to use
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.
1. Ah, financial formulas, the only kind of math that can make money disappear faster than a magician. Anyway, let's tackle this promissory note puzzle, shall we?
To find the proceeds at the time of the sale, we need to subtract the discount from the face value of the note. So, let's do some mathemagics:
Discount = Face Value * Discount Rate * Time
= $12,000 * 0.095 * (30/365) [since August 30 - July 14 = 47 days, but we're only interested in 30 days]
Proceeds = Face Value - Discount
= $12,000 - ($12,000 * 0.095 * (30/365))
And voila! You've got your answer. Now, if only we could use these funny formulas to calculate the value of a clown nose, life would be much simpler.
2. Time for another financial exploration! Let's grab our calculators and dive into the world of T-bills.
(a) To find the purchase price of the T-bill, we need to calculate the discount:
Discount = Face Value * Discount Rate * Time
= $15,000 * 0.0385 * (16/52) [since 16 weeks is a fraction of a year]
Purchase Price = Face Value - Discount
= $15,000 - ($15,000 * 0.0385 * (16/52))
(b) The maturity value of the T-bill is simply the face value:
Maturity Value = Face Value = $15,000
(c) To calculate the interest earned, we subtract the purchase price from the face value:
Interest Earned = Face Value - Purchase Price
= $15,000 - [($15,000 * 0.0385 * (16/52))]
(d) Now, for the effective rate of interest, we need to put our thinking caps on:
Effective Rate of Interest = (Interest Earned / Purchase Price) * (365 / Time)
= [(Face Value - Purchase Price) / Purchase Price] * (365 / Time)
= [(15,000 - (15,000 * 0.0385 * (16/52))) / (15,000 * 0.0385 * (16/52))] * (365 / (16/52))
Now, you've got all the pieces of the financial puzzle! Enjoy crunching those numbers and may the interest rates be ever in your favor. Or at least, not against you.
1. To find the proceeds of a simple discount promissory note, you can use the following formula:
Proceeds = Principal - Discount
Given information:
Principal (P) = $12,000
Simple discount rate (r) = 9%
Term in days (t) = August 30 - July 14 = 47 days
First, calculate the discount:
Discount = Principal * Rate * Time
= $12,000 * 9% * (47/360)
≈ $564.00
Then, calculate the proceeds:
Proceeds = Principal - Discount
= $12,000 - $564.00
≈ $11,436.00
Therefore, the proceeds at the time of the sale would be approximately $11,436.00.
2. To solve this problem, we need to consider the different elements of a Treasury bill (T-bill) transaction.
(a) Purchase price of the T-bill:
Purchase price = Face value - Discount
= Face value * (1 - Discount rate * (t / 360))
Given information:
Face value = $15,000
Discount rate = 3.85%
Term in weeks (t) = 16 weeks
First, convert the term from weeks to days:
t (days) = t (weeks) * 7
= 16 weeks * 7
= 112 days
Then, calculate the purchase price:
Purchase price = $15,000 * (1 - 3.85% * (112 / 360))
≈ $14,641.11
Therefore, the purchase price of the T-bill would be approximately $14,641.11.
(b) Maturity value:
The maturity value of a T-bill is equal to its face value, which is given as $15,000.
Therefore, the maturity value would be $15,000.
(c) Interest earned:
Interest earned = Purchase price - Face value
= $14,641.11 - $15,000
≈ -$358.89
Therefore, the interest earned would be approximately -$358.89.
(d) Effective rate of interest:
To calculate the effective rate of interest, we can use the formula:
Effective rate of interest = (Interest earned / Purchase price) * (360 / t)
Given information:
Interest earned = -$358.89
Purchase price = $14,641.11
Term in days (t) = 112 days
Calculate the effective rate of interest:
Effective rate of interest = (-$358.89 / $14,641.11) * (360 / 112)
≈ -0.0928 or -9.28%
Therefore, the effective rate of interest (to the nearest hundredth of a percent) would be approximately -9.28%.
To solve these problems, we need to understand the concept of simple discount promissory notes and T-bills.
1. A 120-day simple discount promissory note:
- Simple discount promissory notes are similar to loans where the borrower receives less money upfront than the face value of the note, and the lender earns interest when the note is redeemed.
- The formula to calculate the proceeds at the time of the sale is:
Proceeds = Face Value - Discount
In this case:
- Face Value (FV) = $12,000
- Simple Discount Rate (SDR) = 9%
- Discount Rate (DR) = 9.5%
- Time (T) = August 30 - July 14 = 47 days
Now, let's calculate the discount:
- Discount = (Face Value * Simple Discount Rate * Time) / 360
Substitute the given values into the formula to get the discount:
- Discount = (12,000 * 0.09 * 47) / 360
Proceeds = Face Value - Discount
- Proceeds = 12,000 - [ (12,000 * 0.09 * 47) / 360 ]
- Calculate the result to find the proceeds.
2. A $15,000 T-bill:
- T-bills are short-term government securities with a fixed face value and a maturity date. They are typically sold at a discount from their face value and mature after a specified period.
- We need to find the purchase price, maturity value, interest earned, and the effective rate of interest.
In this case:
- Face Value (FV) = $15,000
- Discount Rate (DR) = 3.85%
- Time (T) = 16 weeks
(a) Purchase Price:
- The purchase price is the amount paid to buy the T-bill.
- Purchase Price = Face Value - Discount
- Calculate the purchase price using the given discount rate.
(b) Maturity Value:
- The maturity value is the face value of the T-bill when it matures.
- Maturity Value = Face Value
(c) Interest Earned:
- Interest Earned = Face Value - Purchase Price
- Calculate the interest earned using the purchase price and the face value.
(d) Effective Rate of Interest:
- The effective rate of interest is the interest earned divided by the purchase price, expressed as a percentage.
- Effective Rate of Interest = (Interest Earned / Purchase Price) * 100
- Calculate the effective rate of interest to the nearest hundredth.
Remember to substitute the given values into the formulas to calculate the results for each problem.