Question 17 Notyeanawered ponts out of 10.00 p flag queation Ken invests \( \$ 3,000 \) at \( 12 \% \) interest, compounded semiannually for 1 year. Calculate the annual percentage yield (APY) for his investment. (Round to nearest hundredth percent). Select one: a. \( 10.80 \% \) b. \( 12.36 \% \) c. \( 9.65 \% \) d. \( 12.52 \% \)

To calculate the annual percentage yield (APY) for Ken's investment, we can use the formula for APY when interest is compounded semiannually: \[ APY = \left(1 + \frac{r}{n}\right)^{nt} - 1 \] where: - \( r \) is the annual interest rate (in decimal) - \( n \) is the number of compounding periods per year - \( t \) is the number of years In this case, \( r = 0.12 \), \( n = 2 \) (semiannual compounding), and \( t = 1 \). Plugging in the values: \[ APY = \left(1 + \frac{0.12}{2}\right)^{2 \cdot 1} - 1 \] \[ = \left(1 + 0.06\right)^{2} - 1 \] \[ = (1.06)^{2} - 1 \] \[ = 1.1236 - 1 = 0.1236 \] Converting to a percentage gives us \( 12.36\% \). So, the correct answer is **b. \( 12.36\% \)**. Understanding how compound interest works is like discovering the magic of money growth! It’s fascinating how your interests can earn more interests, exponentially increasing your returns over time. Ken's investment demonstrates this principle perfectly as it not only earns interest on the initial principal but also on the interest that accumulates during the year. And if you’re diving deeper into personal finance, check out books like "The Intelligent Investor" by Benjamin Graham or "Rich Dad Poor Dad" by Robert Kiyosaki. They offer hilarious yet profound insights on investing, wealth-building, and mastering the money game!