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If Allison has saved $1,000,000 upon retirement, how much can she live on each year, if she can...

Question:

If Allison has saved $1,000,000 upon retirement, how much can she live on each year, if she can earn 5% per year, and will end with $0, when she expects to die, 25 years after retirement?

Cash Flows:

Cash flows refer to the money that is expected to be received or spent during a particular period of time. Cash inflow is the money that is earned while cash outflow refers to the money that is being spent. If the money that is earned or spent is constant for a long then it is referred to as an annuity.

Answer and Explanation:

To compute the annual money that Allison require per year we shall use the time value of money formula.

  • {eq}\text{Future value=Annuity*Discounting factor.} {/eq}

The discount rate to be used will be computed as follows:

  • {eq}\text{Discounting Factor}=\dfrac { 1- \frac { 1 }{ (1+r)^n } }{ r } {/eq}

Where r is the interest rate or the interest rate, n is the number of years.

  • {eq}\text{Discounting Factor}=\dfrac { 1- \frac { 1 }{ (1+0.05)^{25} } }{ 0.05 } {/eq}
  • {eq}\text{Discounting Factor}=14.09394457 {/eq}
  • {eq}1000000=\text{Annuity}*14.09394457 {/eq}

Therefore, the annual money required will be:

  • {eq}\text{Annuity}=\dfrac{1000000}{14.09394457} {/eq}
  • {eq}\text{Annuity}=$70,952.4573 {/eq}

Allison will have to use $70,952.4573 annually to exhaust his investment within 25 years.


Learn more about this topic:

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What is Annuity? - Definition & Formula

from Corporate Finance: Help & Review

Chapter 2 / Lesson 7
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