In Exercises \( 23-28 \), an account has a rate of \( 3.5 \% \). Find th effective annual yield, rounded to the nearest humdredth of. percent. if the interest is compounded 23. semiannually.

To find the effective annual yield with semiannual compounding at a rate of 3.5%, you can use the formula for effective annual yield (EAY): \[ EAY = \left(1 + \frac{r}{n}\right)^{nt} - 1 \] where \( r \) is the nominal interest rate (0.035), \( n \) is the number of compounding periods per year (2 for semiannual), and \( t \) is the number of years (1 for one year). Plugging in the values: \[ EAY = \left(1 + \frac{0.035}{2}\right)^{2 \cdot 1} - 1 \approx 0.071167 \] Converting this to a percentage gives approximately 7.12%. So, the effective annual yield, rounded to the nearest hundredth of a percent, is 7.12%. In the world of finance, understanding effective annual yield is crucial. It helps investors gauge how much they can earn on their investments over a year, taking into account the effects of compounding interest. Knowing the effective yield can influence your choices, whether you are looking to save, invest or take out a loan. When dealing with compounded interest, a common mistake is to simply use the nominal rate without considering the effects of compounding periods. Always remember that compounding frequency can significantly affect your returns, so adjust calculations accordingly to ensure you're on the right financial track!