Final answer:
Using the future value of an annuity formula, the account will have $140,105.38 at the end of 25 years, given a $2,000 annual investment at 5.5% interest compounded annually; none of the provided answer choices are correct.
Step-by-step explanation:
To determine how much will be in the 401K account at the end of 25 years with an annual investment of $2,000 at 5.5% interest compounded annually, we can use the future value of an annuity formula:FV = P × { [((1 + r)^n - 1) / r] }
Where FV is the future value, P is the payment (annual contribution), r is the annual interest rate (as a decimal), and n is the number of periods.For this problem .Substituting these values into the formula, we get:
FV = 2,000 × { [((1 + 0.055)^25 - 1) / 0.055] }Calculating this gives us:FV = 2,000 × { [((1.055)^25 - 1) / 0.055] }FV = 2,000 × { [4.292898 - 1) / 0.055] }FV = 2,000 × 70.0526891FV = $140,105.38Therefore, none of the provided choices (a, b, c, d) are correct. The correct answer is that the account will have $140,105.38 at the end of 25 years.
To find out how much your account will have at the end of 25 years, you can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value of the account, P is the principal (the initial investment), r is the interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years. In this case, the principal is $2,000, the interest rate is 5.5% (or 0.055), and the interest is compounded annually. Plugging in these values, we get A = 2000(1 + 0.055/1)^(1*25). After calculating this, we find that the account will have approximately $158,614.02 at the end of 25 years.