Final answer:
The value of a $5,500 retirement account with a 10% annual interest rate after 5 years, calculated using the compound interest formula, will be approximately $8,857.81. None of the provided options match this correct value, suggesting an error in the question's listed options.
Step-by-step explanation:
The subject of this question is personal finance, a topic often included in high school mathematics and business curriculums. Specifically, the question deals with compound interest and how it applies to retirement savings. The compound interest formula is used to calculate the future value of an investment after a certain number of years given a certain annual interest rate. The formula for compound interest is A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), and n is the number of years the money is invested. The question asks us to calculate the value of a $5,500 contribution to a retirement account after 5 years at an annual interest rate of 10% with no additional contributions.
Using the compound interest formula:
A = P(1 + r)^n
A = $5,500(1 + 0.10)^5
A = $5,500(1.10)^5
A = $5,500(1.61051)
A = $8,857.81
The value of the retirement account after 5 years will be approximately $8,857.81, which is not one of the options provided in the question. It appears that there is a mistake in the options listed within the question.