what is the annual percentage yield (apy) of a simple discount note for $7000 at a bank discount rate of 6% for 3 months?
To calculate the annual percentage yield (APY) of a simple discount note, you first need to calculate the discount interest and then convert it to an annual percentage rate (APR).
The formula to calculate the discount interest is:
Discount Interest = Principal Amount x Discount Rate x Time
Given:
Principal Amount (P) = $7000
Discount Rate (R) = 6% (or 0.06 as a decimal)
Time (T) = 3 months (or 0.25 in terms of a year since 3 months is 1/4th of a year)
Using the formula, we can calculate the discount interest:
Discount Interest = $7000 x 0.06 x 0.25 = $105
Next, we need to convert the discount interest to an annual percentage rate (APR).
The formula to convert discount interest to APR is:
APR = Discount Interest ÷ Principal Amount x Time
Using the calculated discount interest ($105), we can calculate the APR:
APR = $105 ÷ $7000 x 0.25 = 0.0015
Finally, we can convert the APR to an annual percentage yield (APY) by multiplying it by 100:
APY = APR x 100 = 0.0015 x 100 = 0.15%
Therefore, the annual percentage yield (APY) of the simple discount note for $7000 at a bank discount rate of 6% for 3 months is 0.15%.