SOLUTION: You want to be able to withdraw $20,000 from your account each year for 20 years after you retire. You expect to retire in 25 years. If your account earns 5% interest, how mu

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Question 1174080: You want to be able to withdraw $20,000 from your account each year for 20 years after you retire.
You expect to retire in 25 years.
If your account earns 5% interest, how much will you need to deposit each year until retirement to achieve your retirement goals?

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
You want to be able to withdraw $20,000 from your account each year for 20 years after you retire.
You expect to retire in 25 years.
If your account earns 5% interest, how much will you need to deposit each year until retirement to achieve your retirement goals?
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Solution


Step  1.

First, I will determine how much money X should be accumulated on the account during 25 years to the time  of retiring,
in order for to have enough to withdraw $20000 at the beginning of each year for 20 years.


By withdrawing $20000 each year, my compound account (the remaining money) still earns 5% per annum,  so everything works as it was 

considered/described at the lesson  Withdrawing a certain amount of money periodically from a compounded saving account  in this site.


Thus the formula for the account value before it starts recharging is

    X = 20000%2A%28%28%281-%281%2B0.05%29%5E%28-20%29%29%29%2F0.05%29,     (1)


which gives us the value at the account of

    X  = 249244.21 dollars.


Step  2.

Now I am in position to determine how much I should deposit at the end of each year during 25 years to the starting moment of the retiring
to accumulate  249244.21 dollars in my account. 


It is the standard Annuity saving plan, and the formula is

    249244.21 = D%2A%28%28%281%2B0.05%29%5E25-1%29%2F0.05%29,     (2)


where D is the annual deposit amount.


The multiplier  %28%281%2B0.05%29%5E25-1%29%2F0.05 = 47.7271,


which implies from equation (2)  that  D = 249244.21%2F47.7271 = 5222.28  dollars.


It is your answer:  During 25 years, you should deposit $5222.28 at the end of each year to your account,

                    in order for to withdraw $20000 annually from yours account for 20 years after your retiring.

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My lessons in this site associated with annuity saving plans and retirement plans are

    - Geometric progressions
    - The proofs of the formulas for geometric progressions

    - Ordinary Annuity saving plans and geometric progressions
    - Annuity Due saving plans and geometric progressions
    - Solved problems on Ordinary Annuity saving plans
    - Withdrawing a certain amount of money periodically from a compounded saving account
    - Miscellaneous problems on retirement plans

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Geometric progressions".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.