An account has a rate of 3.5%. Find the effective annual yield of the interest is compounded semiannually.
To find the effective annual yield (EAY) when the interest is compounded semiannually, we can use the formula:
EAY = (1 + r/n)^n - 1
Where:
- r is the annual interest rate (as a decimal)
- n is the number of times the interest is compounded per year
In this case, the annual interest rate is 3.5% or 0.035 as a decimal, and the interest is compounded semiannually, meaning it is compounded twice a year (n = 2).
EAY = (1 + 0.035/2)^2 - 1
EAY = (1 + 0.0175)^2 - 1
EAY = (1.0175)^2 - 1
EAY = 1.03550625 - 1
EAY = 0.03550625
Therefore, the effective annual yield of the account is 0.03550625, or 3.550625% when the interest is compounded semiannually.