Retierment Problem Illlustrating the use of Time Value of Money. Page 1. Debbie
recently graduated from NC State University with a BS degree in Electrical ...
Retierment Problem Illlustrating the use of Time Value of Money Debbie recently graduated from NC State University with a BS degree in Electrical Engineering. She is gainfully employed by GoPack Computing located in Research Triangle Park. Debbie is 25 and plans to retire at 65 or 40 years from now. She wants to travel during her retirement and has decided to start saving now. She can save $200 per month for the next ten years then she plans to increase her savings to $500 per month for the remaining 30 years. How much can Debbie withdraw each month during her retirement? Assume she will live for 20 years after retirement and withdraws all of the money in the account. She will earn 12% during the saving period and 6% during retirement. Assume monthly compounding during the savings and retirement periods. Frank recently graduated from MIT with a Ph.D. in Physics. He has started an investment company applying his mathematical knowledge to valuing assets. Frank is 40 and plans to retire at 65 or 25 years from now. He wants to travel much like Debbie during his retirement and must start saving now. How much must he save per month for the next 25 years to be able to withdraw $24,368.98 per month? Assume he will live for 20 years after retirement and withdraws all of the money in the account. He will earn 12% during the saving period and 6% during retirement. Assume monthly compounding during the savings and retirement periods.
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Retierment Problem Illlustrating the use of Time Value of Money Answer to the first problem 0
i = 12% 10
A = 200
V40
60
A = 500
=
200(FVIFA(10)(12), (12%)/(12))(FVIF(30)(12),(12%)/(12))+500(FVIFA(30)(12),(12%)/(12))
=
200(FVIFA(120),(1%))(FVIF(360),(1%))+500(FVIFA(360),(1%))
=
(200)(230.0387)(35.9496) + (500)(3494.9641)
=
$3,401,441.90
$3,401,441.90 =
A(PVIFA(20)(12),(6%)/(12))
$3,401,441.90 =
A(PVIFA(240),(0.5%))
$3,401,441.90 =
A(139.5808)
A
A=? i = 6%
40
=
$24,368.98
Answer to the second problem 25
i = 12%
A = $24,368.98 i = 6%
45
A=?
V25
=
$24,368.98(PVIFA(20)(12),(6%)/(12))
=
$24,368.98(PVIFA(240),(0.5%))
=
$24,368.98(139.5808)
=
$3,401,441.90
$3,401,441.90 =
A
=
A(FVIFA(25)(12),(12%)/(12)) =
A(FVIFA(300),(1%))
=
A(1878.8466)
$1,810.39
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