etermine the annual percentage yield, or the effective interest rate, for $1000 invested at 3.45% over 15 years compounded daily. Round your answer to the nearest hundredth of a percent, if necessary.
To calculate the annual percentage yield (APY) or effective interest rate for $1000 invested at 3.45% over 15 years compounded daily, we can use the formula for compound interest:
APY = (1 + r/n)^(n) - 1
Where:
r = annual interest rate (as a decimal)
n = number of compounding periods in a year
Given:
r = 3.45% = 0.0345
n = 365 (since it is compounded daily)
APY = (1 + 0.0345/365)^(365) - 1
APY = (1 + 0.000094)^(365) - 1
APY = (1.000094)^(365) - 1
APY = 1.036194 - 1
APY = 0.036194
Therefore, the annual percentage yield for $1000 invested at 3.45% over 15 years compounded daily is approximately 3.62%.