You believe you will spend $40,000 per year for 20 years once you retire in 40 years. If the...

Question:

You believe you will spend $40,000 per year for 20 years once you retire in 40 years. If the interest rate is 5 per cent per year. how much must you save each year until retirement to meet your retirement goal?

Value of an Annuity:

The value of an annuity is determined through the use of formulas that incorporate the time value of money concept. An annuity is an equal amount of cash flows that may occur at the start or at the end of a period. In calculating the value of an annuity the interest rate, time period and compounding periods have to be taken into consideration.

Answer and Explanation: 1

At retirement, the present value of the $40,000 annuity will be:

  • {eq}Present \ Value \ of \ ordinary \ annuity = Annuity * \dfrac{(1 - (1 + r )^{-n}) }{ r} {/eq}
  • {eq}Present \ Value \ of \ ordinary \ annuity = 40,000 * \dfrac{(1 - (1 + 0.05)^{-20}) }{ 0.05} {/eq}
  • {eq}Present \ Value \ of \ ordinary \ annuity = 40,000 * 12.46221034 {/eq}
  • {eq}Present \ Value \ of \ ordinary \ annuity = $498,488.41 {/eq}

The $498,488.41 represents the future value of the annual savings:

  • {eq}FV \ of \ ordinary \ annuity = Annuity * \dfrac{(1+ r ) ^n - 1}{ r} {/eq}
  • {eq}498,488.41 = Annuity * \dfrac{(1+ 0.05 ) ^{40} - 1}{ 0.05} {/eq}
  • {eq}498,488.41 = Annuity * 120.7997742 {/eq}
  • {eq}Annuity = \dfrac{498,488.41}{ 120.7997742} {/eq}
  • {eq}Annuity = $4,126.57 {/eq}

Learn more about this topic:

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How to Find the Value of an Annuity

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Chapter 21 / Lesson 15
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An annuity is a type of savings account that pays back the investor in the future. Learn the formula used to calculate an annuity's value, and understand the importance of labeling specific numbers to calculate an output over time.


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