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For the three-part question that follows, provide your answer to each part in the given workspace. Identify...

For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Zach invests $500 at the end of each month into a mutual fund. The mutual fund contains stocks that are expected to yield 6.0% per year.
Part A: Calculate the future value of the mutual fund after 12 months. The factor from the Future Value of Ordinary Annuity table is 12.33556. Show your work.
Part B: Calculate the future value of the mutual fund after 30 months. The factor from the Future Value of Ordinary Annuity table is 32.32002. Show your work.
Part C: Write a complete sentence to explain how the factor from the Future Value of Ordinary Annuity table can be found if it is not given to you. Be sure to include what is needed to find the factor.

Answer

  1. Part A:

    The future value of the mutual fund after 12 months is calculated as follows:
    Future Value = Monthly Investment × Future Value Annuity Factor
    Future Value = $500 × 12.33556 = $6,167.78

  2. Part B:

    The future value of the mutual fund after 30 months is calculated as follows:
    Future Value = Monthly Investment × Future Value Annuity Factor
    Future Value = $500 × 32.32002 = $16,160.01

  3. Part C:

    The factor from the Future Value of Ordinary Annuity table can be found by using the formula for the future value of an ordinary annuity, which involves the interest rate per period and the number of periods. Specifically, the factor is calculated using the formula:
    FV Annuity Factor = [(1 + r)^n - 1] / r
    where r is the monthly interest rate and n is the number of periods.

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