Final answer:
To calculate the effective rate (APY) of interest for 1 year, we need to use the formula for compound interest. By plugging the given values into the formula and solving for the final amount, we can find the effective rate (APY) of interest.
Step-by-step explanation:
To calculate the effective rate (APY) of interest, we need to consider the compounding frequency. In this case, the interest is compounded quarterly. The formula for compound interest is A = P(1 + r/n)^(NT), where A is the final amount, P is the principal, r is the interest rate, n is the number of times compounded per year, and t is the number of years.
Using the given values, we have P = $15,500, r = 6% or 0.06, n = 4 (quarterly compounding), and t = 1 year. Plugging in these values into the formula, we get A = $15,500(1 + 0.06/4)^(4*1). Solving this equation gives us the final amount after 1 year, and the effective rate (APY) of interest is the difference between the final amount and the principal.
After calculating, the final amount is $16,117.08. Therefore, the effective rate (APY) of interest for 1 year is $16,117.08 - $15,500 = $617.08.