Final answer:
Alicia's savings account with $800 at 6% annual interest compounded quarterly will amount to approximately $848.24 at the end of one year, which is option A) $848.24.
Step-by-step explanation:
The question asks for the final amount in Alicia's savings account with a principal of $800, an annual interest rate of 6%, compounded quarterly after one year. To calculate the compound interest for this scenario, we can use the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
Given the values: P = $800, r = 0.06 (6% annual interest), n = 4 (quarterly compounding), and t = 1 (one year), we can calculate A as follows:
A = $800(1 + 0.06/4)^(4*1) = $800(1 + 0.015)^4 = $800 * 1.061363 => approximately $848.24.
Therefore, the answer is A) $848.24.
Understanding compound interest is essential in personal finance, as it can impact savings growth over time significantly. Unlike simple interest, compound interest is calculated on the initial principal, including all the accumulated interest from previous periods. This effect can lead to a significant increase in the savings balance, which is illustrated by comparing the results of compound versus simple interest over the same period.