Math Problem Statement
Shaylea, age 22, just started working full-time and plans to deposit $5 comma 000 annually into an IRA earning 7 percent interest compounded annually. How much would she have in 20 years, 30 years, and 40 years? If she changed her investment period and instead invested $416.67 monthly, and the investment also changed to monthly compounding, how much would she have after the same three time periods? Comment on the differences over time. Question content area bottom Part 1 Click the table icon to view the future value FVIFA table: LOADING.... With annual investments and compounding, after 20 years, Shaylea would have $ enter your response here. (Round to the nearest cent.) Part 2 With annual investments and compounding, after 30 years, Shaylea would have $ enter your response here. (Round to the nearest cent.) Part 3 With annual investments and compounding, after 40 years, Shaylea would have $ enter your response here. (Round to the nearest cent.) Part 4 With monthly investments and monthly compounding interest, after 20 years, Shaylea would have $ enter your response here. (Round to the nearest cent.) Part 5 With monthly investments and monthly compounding interest, after 30 years, Shaylea would have $ enter your response here. (Round to the nearest cent.) Part 6 With monthly investments and monthly compounding interest, after 40 years, Shaylea would have $ enter your response here. (Round to the nearest cent.) Part 7 The differences are: (Select the best choice below.) A. the longer the money is invested, the more you will have in the future. The number of compounding periods does not have any effect on the investment. B. the longer the money is invested, the more you will have in the future. The more compounding periods you have in a given time, the more money you will have in the future. C. the longer the money is invested the more you will have in the future. The more compounding periods you have, the less money you will have in the future because the interest rate is lower. D. the longer the money is invested, the less you will have in the future because the interest rate does not change with the cost of living.
Solution
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Math Problem Analysis
Mathematical Concepts
Future Value of Annuities
Compounded Interest
Financial Mathematics
Formulas
Future Value of an Annuity (annual compounding): FV = P * ((1 + r)^n - 1) / r
Future Value of an Annuity (monthly compounding): FV = P * ((1 + r/m)^(n*m) - 1) / (r/m)
Theorems
Time Value of Money
Suitable Grade Level
Undergraduate/College-level Financial Mathematics
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