Garrett deposits $8000. Determine the APY if there is an APR of 3% compounded daily. Express your answer as a percentage rounded to the nearest hundredth of a percent, if necessary.
To find the APY, we first need to calculate the effective annual rate (EAR) using the formula:
EAR = (1 + (APR / n))^n - 1
Where:
APR = 3% = 0.03
n = number of compounding periods per year = 365
EAR = (1 + (0.03 / 365))^365 - 1
EAR = (1 + 0.00008219178)^365 - 1
EAR = 1.00008219178^365 - 1
EAR = 1.031327167 - 1
EAR = 0.031327167
Now, we can find the APY using the formula:
APY = (1 + EAR)^n - 1
APY = (1 + 0.031327167)^1 - 1
APY = 1.031327167 - 1
APY = 0.031327167
Converting the APY to a percentage:
APY = 0.031327167 * 100
APY = 3.13%
Therefore, the APY in this case is 3.13%.