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Retirement Plan Assignment

Question: Bob and Lisa are both married, working adults. They both plan for retirement and consider the $2,000 annual contribution a must.

Create a chart summarizing the details of the investment for both Bob and Lisa. Explain the results in terms of time value of money.

Summary of BOB and LISA's Investment in IRA

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Solution:

Assessment for LISA

Currently, LISA is 32 years of age and she started her investments of $2,000 per annum she was 20. By the age of 32, she has already made 13 annual payments and then she left her job but she kept her accumulated funds invested till age 65.

This is an annuity and hence how much funds she has been able to create must be assessed with the help of future value of the annuity.
Amount of Annuity = $2,000
N= 13
Rate of return = 7%
The future value of annuity (ate age 32) is estimated as follows:
FV = Annuity * FVAF (r%,n)
FV = $2,000* FVAF (7%,13)
FV = $2,000* 20.14064
FV = $40,281.28
So LISA was able to create a corpus of $40,281.28 when she left her job but she left the investment in IRA for another 33 years as she wanted to withdraw when she becomes 65 years of age.
This means the initial fund of $40,281.28 stayed invested for 33 more years.
N= 33
R= 7%
Future value of this investments made by LISA is estimated as follows:

FV = PrincipalInvested *(1+r%)^33
FV = Principal Invested *FVF (7%,33)
FV = $40,281.28 *FVF (7%,33)
FV = $40,281.28 * 9.32534
FV = $375,636.6(Eugene Brigham & Michael Ehrhardt, 2010)
As can be seen from the above estimations the future value accumulated in Lisa's fund is $375,636.6

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Assessment for BOB

Currently, BOB is 32 years of age and he starts saving $2,000 till he is of the age of 65. This means he makes 33 contributions of $2,000 each. This is an annuity and hence how much funds he has been able to create must be assessed with the help of future value of the annuity.
Amount of Annuity = $2,000
N=33
Rate of return = 7%
The future value of annuity is estimated as follows:
FV = Annuity * FVAF (r%,n)
FV = $2,000* FVAF (7%,33)
FV = $2,000* 118.9334
FV = $237,866.80
So if BOB is able make these 33 annual payments of $2,000 into his IRA account then he would be able to have a fund balance of $237,866.80 when he is 65years of age.

Discussion of the Amount's accumulated funds estimated above for LISA & BOB

As can be seen from the above estimations the future value accumulated in Lisa's fund is $375,636.6. However, BOB is able to have a fund balance of $237,866.80 when he is 65years of age. This means LISA would have higher funds as compared to BOB. It seems that BOB has made more investments than Lisa on the face of it. LISA has made only 13 payments to the funds, but BOB has made 33 payments.

However, LISA is able to generate a higher accumulated balance because of the simple reason that she had invested early and invested for a higher investment horizon. By the time BOB started investing in IRS Lisa already have accumulated $40,281. As a result, of which she was able to generate more compounding of the amount and more returns in all the next 33 years. So, if one wants to be able to take advantage of the time value of moony then one shall start investing early and invest for a longer duration as well(ROSS and Westerfield, 2012).

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