Determine the annual percentage yield, or the effective interest rate, for $200 invested at 6.64% over 10 years compounded daily. Round your answer to the nearest hundredth of a percent, if necessary.
To calculate the annual percentage yield, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money).
r = the annual interest rate (decimal).
n = the number of times the interest is compounded per year.
t = the number of years the money is invested for.
Given:
P = $200
r = 6.64% or 0.0664 (6.64%/100)
n = 365 (compounded daily)
t = 10 years
A = 200(1 + 0.0664/365)^(365*10)
A = 200(1 + 0.0001819186158)^(3650)
A = 200(1.0001819186158)^(3650)
A = 200(2.02215184409605)
A = $404.43
Now, we can calculate the annual percentage yield by using the formula:
APY = (A/P)^(1/t) - 1
APY = ($404.43/$200)^(1/10) - 1
APY = 2.02215^(0.1) - 1
APY = 1.06805472394 - 1
APY = 0.06805472394
Therefore, the annual percentage yield, or the effective interest rate, for $200 invested at 6.64% over 10 years compounded daily is approximately 6.81%.