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You are planning to save for retirement over the next 25 years. To do this, you will invest $820...

Question:

You are planning to save for retirement over the next 25 years. To do this, you will invest $820 per month in a stock account and $420 per month in a bond account. The return of the stock account is expected to be 10.2%, and the bond account will pay 6.2%. When you retire, you will combine your money into an account with a 7.2% return. How much can you withdraw each month from your account assuming a 20-year withdrawal period? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Saving for Retirement:

Saving for retirement is often achieved through periodic contributions to a saving account that provides positive returns. The stream of contributions to the savings account constitute an annuity, and the future value of this annuity is the amount of funds available for post-retirement expenses.

Answer and Explanation: 1

You can withdraw $8,672.70 each month from your account.

We first compute the future value your savings at retirement. Both accounts will have 25 * 12 = 300 contributions. The future value of the savings in the stock account is:

  • {eq}\displaystyle \frac{820*((1 + 10.2\%/12)^{300} - 1)}{10.2\%/12} = 1,125,795.30 {/eq}

The future value of the bond account is:

  • {eq}\displaystyle \frac{420*((1 + 6.2\%/12)^{300} - 1)}{6.2\%/12} = 300,181.33 {/eq}

Thus the total value of your retirement account = 1,125,795.30 + 300,181.33 = 1,425,976.63. After retirement you will need monthly expenses for 20 years, or 12 * 20 = 240 monthly withdrawals. At a 7.2% annual rate, the monthly discount rate is 7.2% / 12 = 0.6%. The monthly withdrawal is:

  • {eq}\displaystyle \frac{ 1,425,976.63*0.6\%}{1 - (1 + 0.6\%)^{-240}} = 8,672.70 {/eq}

Learn more about this topic:

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How to Calculate Future Value: Formula & Example

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Chapter 5 / Lesson 16
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Understand the definition of future value and the future value formula. Explore some examples that show how to calculate the future value of an investment.


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