You and your wife are making plans for retirement. You plan on living 25 years after you retire and would like to have $90,000 annually

You and your wife are making plans for retirement. You plan on living 25 years after you retire and would like to have $90,000 annually on which to live. Your first withdrawal will be made one year after you retire and you anticipate that your retirement account will earn 10% annually.

What amount do you need in your retirement account the day you retire? Round your answer to the nearest cent. Do not round intermediate calculations.

Assume that your first withdrawal will be made the day you retire. Under this assumption, what amount do you now need in your retirement account the day you retire? Round your answer to the nearest cent. Do not round intermediate calculations.

 

 

answer:

Amount needed in retirement account the day I retire:
When First Annual withdrawl is one year after I retire $ 8,16,933.60
When First Annual withdrawl is the day I retire $ 8,98,626.96
Working:
On the date of retirement we must have amount equal to present value of future withdrawl.
In other words, on the date of retirement we have present value of Annual withdrawl of $ 90,000 for 25 Years.
1) When First annual withdrawl is one year after I retire
Present Value = Annual Withdrawl*cumulative discount factor
= 90000*9.077
= $ 8,16,933.60
Cumulative discount factor = ((1-(1+i)^-n)/i) Where,
= ((1-(1+.10)^-25)/.10) i = annual return = 10%
= 9.077 n = Life = 25 Years
2) When first annual withdrawl is the day I retire
Present Value = Annual Withdrawl*cumulative discount factor
= 90000*9.985
= $ 8,98,626.96
Cumulative discount factor = ((1-(1+i)^-n)/i)*(1+i) Where,
= ((1-(1+.10)^-25)/.10)*(1+.10) i = annual return = 10%
= 9.985 n = Life = 25 Years
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