Final answer:
The effective annual interest rate for the account represented by the expression 1,000(1.0215)^4t is 8.91%. This is found by considering the nominal rate compounded quarterly, using the formula for EAR when interest is compounded n times a year.
Step-by-step explanation:
The expression 1,000(1.0215)4t represents the amount of money in an account after t years with compound interest. The effective annual interest rate is found by looking at how the principal grows over one year, without considering the effects of compounding within the year. Since the base of the exponent is 1.0215 and it is raised to the power of 4, this means that the interest is compounded quarterly. To find the effective annual interest rate (EAR), we would need to look at the amount the initial sum grows to over one exact year. The formula for EAR when interest is compounded n times a year is (1 + (nominal rate / n))n - 1. In this case, the nominal annual interest rate is compounded quarterly (4 times a year), so n=4.
Using the formula EAR = (1 + (nominal rate / n))n - 1, with a nominal rate = 1.02154 - 1 (that's the entire 1.0215 term to the power of 4), we can calculate the EAR:
EAR = (1.02154) - 1 = 1.0891 - 1 = 0.0891 or 8.91%.
Therefore, the effective annual interest rate for the account is 8.91%.