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The company you work for will deposit $150 at the end of each month into your retirement fund....

Question:

The company you work for will deposit $150 at the end of each month into your retirement fund. Interest is compounded monthly. You plan to retire 25 years from now and estimate that you will need to withdraw $2,000 per month during retirement, which will last 30 years. If the account pays 12% compounded monthly, how much do you need to put into the account each month, in addition to your company's deposit, in order to meet your retirement needs?

Retirement Planning:

Retirement planning is a lifelong process. The earlier an individual starts to plan for retirement, the easier this process will be. This is so because earlier savings accumulate interest for a longer period of time than later payments.

Answer and Explanation: 1

Let,

  • r = interest rate = 12% / 12 = 1% per month
  • n = number of saving months = 25 * 12 = 300
  • k = number of spending months = 30 * 12 = 360
  • PV = present value of annuity
  • FV = future value of annuity
  • p = employer contribution = $150
  • q = your contribution = ?

Your savings for retirement must be equal to the value of your spending stream. Therefore, the future value of savings is equal to the present value of spending:

{eq}FV(Saving \ n \ periods)=PV(Spending \ k \ periods)\\ Saving*\frac{(1+r)^{n}-1}{r}=Spending*\frac{1-(1+r)^{-k}}{r}\\ (p+q)*\frac{(1+r)^{n}-1}{r}=Spending*\frac{1-(1+r)^{-k}}{r}\\ (150+q)*\frac{(1+0.01)^{300}-1}{0.01}=2,000*\frac{1-(1+0.01)^{-360}}{0.01}\\ q=-\$46.51\\ {/eq}

Since the number you need to deposit is negative, you can withdraw $46.51 per month before retirement.


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
9.4K

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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