kate davidson signed a simple discount note for $9000. the discount rate is 5%, and the term of the note is 18 months. what is the annual percentage yield (apy)?
5.4%
To calculate the annual percentage yield (APY) of the simple discount note, we need to first calculate the discount, which is the difference between the face value and the present value of the note.
The formula to calculate the present value (PV) of a simple discount note is:
PV = FV - D
Where:
PV = Present Value
FV = Face Value (the amount due at maturity)
D = Discount
In this case, the Face Value (FV) is $9000, and the Discount (D) can be calculated using the discount rate and the term.
Discount = FV * Rate * Time
Where:
Rate = Discount Rate (as a decimal)
Time = Term
In this case, the Discount Rate is 5% (0.05) and the Term is 18 months.
Discount = $9000 * 0.05 * (18/12)
Discount = $675
Now we can calculate the Present Value (PV):
PV = $9000 - $675
PV = $8325
To find the APY, we need to determine the interest earned over the term of the note and convert it to an annual percentage.
Interest Earned = Face Value - Present Value
Interest Earned = $9000 - $8325
Interest Earned = $675
APY = (Interest Earned / Present Value) * (365 / Term)
APY = ($675 / $8325) * (365 / 18)
APY ≈ 0.0811 or 8.11%
Therefore, the annual percentage yield (APY) for the simple discount note is approximately 8.11%.
To calculate the Annual Percentage Yield (APY), we need to first find the discount and then use it to calculate the APY. Here are the step-by-step calculations:
Step 1: Calculate the discount amount.
Discount = Principal Amount * Discount Rate * Time
Discount = $9,000 * 0.05 * (18/12) [converting months to years]
Discount = $900
Step 2: Calculate the proceeds.
Proceeds = Principal Amount - Discount
Proceeds = $9,000 - $900
Proceeds = $8,100
Step 3: Calculate the APY.
APY = (Discount / Proceeds) * (365 / Time) * 100%
APY = ($900 / $8,100) * (365 / 1.5) * 100%
APY = (0.1111) * (243.33) * 100%
APY = 27.0375%
Therefore, the Annual Percentage Yield (APY) for the simple discount note is approximately 27.04%.