Kate Davidson signed a simple discount note for $9,000. The discount rate is 5%, and the term of the note is 18 months. What is the annual percentage yield (APY)?
To calculate the annual percentage yield (APY), we first need to calculate the maturity value and then use the formula:
APY = (Maturity Value - Principal) / Principal * (365 / Total Days)
Here's how you can calculate the APY:
Step 1: Calculate the discount.
Discount = Principal * Discount Rate * Term
= $9,000 * 0.05 * 18/12
= $675
Step 2: Calculate the maturity value.
Maturity Value = Principal - Discount
= $9,000 - $675
= $8,325
Step 3: Calculate the Total Days.
Since the term is given in months, we need to convert it into days.
Total Days = Term * 365
= 18/12 * 365
= 273
Step 4: Calculate APY.
APY = (Maturity Value - Principal) / Principal * (365 / Total Days)
= ($8,325 - $9,000) / $9,000 * (365 / 273)
= -$675 / $9,000 * 1.338
= -0.075 * 1.338
= -0.10065
The calculated APY is approximately -10.065%.
Note: A negative APY indicates a loss on investment. It is unusual for a simple discount note to have a negative APY, so please double-check the calculations or review the given information.