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

Interest Compounding
Future Value of Annuities
Time Value of Money

Formulas

Future Value of Annuity Formula (Annual Compounding): FV = P * ((1 + r)^t - 1) / r
Future Value of Annuity Formula (Monthly Compounding): FV = P * ((1 + (r/12))^(12*t) - 1) / (r/12)

Theorems

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Suitable Grade Level

College Level