Compute the annual saving needed to reach that future value

So, first compute the amount that you must have in your retire-ment fund at age 65 to be able to withdraw $35,000 per year for 20 years. Remember, the money you have in the account will continue to earn 3% a year, after inflation, as long as it’s in the account.

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COMPUTING THE AMOUNT YOU NEED

To calculate the amount needed, we can either use a formula or the Worry-Free Investing (WFI) calculator at our companion Web site.

The formula is:^*

PV stands for the present value of the stream of benefits, i for the interest rate, n for the number of years, and X for the annual benefit.

In our case i is.03, n is 20, and X is $35,000. Substituting them into the formula, you find that the present value is:

Let’s use the online WFI calculator to do this:

WFI Calculations for Amount Needed at Retirement

Number of years 20

Interest rate 3%

Target retirement income $35,000 Amount required at retirement $520,712

PV i

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Worry-Free Investing

A Safe Approach to Achieving Your Lifetime Financial Goals

Thus, you need $520,712 in your account the day you retire to generate $35,000 a year for 20 years, assuming your investments earn 3% return after inflation.

The next step is to calculate how much of your preretirement salary to save each year to reach that goal. You have 30 years until you retire, and you plan to contribute part of your annual salary to your retirement fund each year.By the time you retire, you need to have

$520,712. Again, we are assuming you will earn a real interest rate of 3% per year.

We can use the formula we learned in Chapter 2 to find the annual contribution needed to reach a desired future value:^†

FV stands for future value, i for the interest rate, n for the number of years, and X for the annual contribution. In this case, FV is

$520,712, i is.03, and n is 30. Substituting these figures into the formula, you find that the annual contribution X is $10,626:

Using the online WFI calculator at our Web site (www.prenhall.com/

worryfree/) to do this, you find:

COMPUTING THE AMOUNT YOU NEED

FV i i

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Chapter 3

Reaching Your Retirement Goal

To take account of inflation, you compute the saving rate as a proportion of salary. This is because salaries generally increase at about the rate of inflation, or slightly faster. However, if you are in a declining industry, this might not be so. Assuming you are in a healthy industry, and ignoring the possibility of raises due to promotions, you divide $10,626 by your salary of $50,000, which is 21.25%. Thus, if you save 21.25% of your salary each year, you would be able to pay yourself a retirement income equal to 70%

of your preretirement income, or $35,000. Like Social Security benefits, this income will increase in dollar amount each year to

WFI Calculations for Annual Contributions Required

Number of years 30

Interest rate 3%

Target future value $520,712 Annual contribution required $10,626

Thus, in order to be able to take out a retirement benefit of $35,000 per year for 20 years, you would need to save $10,626 per year in each of the next 30 years.

*. This is the formula for the present value of an ordinary annuity. This means payments start at the end of the year.

†. This is the formula for the future value of an immediate annuity. This means contribu-tions start immediately, at the beginning of the year.

COMPUTING THE AMOUNT YOU NEED

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Worry-Free Investing

A Safe Approach to Achieving Your Lifetime Financial Goals

maintain its purchasing power no matter what the rate of infla-tion turns out to be.

Prices of specific goods and services may rise higher than the rate of inflation, but in general they, too, keep pace with the rate of inflation enough for the purposes of your financial planning and goal setting. While inflation varies somewhat depending on where you live and what stage of life you are in, this approach will bring you very close to protecting your retire-ment purchasing power. If you should move before or during retirement to a low-cost area, you may even come out a little ahead.

In this example, we assumed your salary was $50,000, but suppose it is $100,000. Again, we assume your salary keeps pace with inflation, no more, no less. To achieve a 70% replacement rate by retirement age, you will have to save 21.25% of your salary just like the person who earns $50,000, provided all the other assumptions hold true (i.e., you have 30 years to go before retire-ment age, a life expectancy of 20 years after retireretire-ment, and the real interest rate is 3% per year). In fact, no matter what your salary is, the required saving rate will be the same 21.25% because the required saving rate depends only on the number of years you have to save before retirement, the number of years you will live after retirement, and the real interest rate.

Table 3.1 shows the fraction of your salary you must save for dif-ferent numbers of years before and after retirement if the real interest rate is 3%.

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Thus, you see from Table 3.1 that with a life expectancy of 20 years after retirement, you would have to save 29% of your salary if you started saving 25 years before retirement instead of 30 years before retirement. That sounds impossible. Who can save 29% of income every year after all of the expenses of daily living?

Even those noted savers, the Japanese, don’t save that much.

Relax. Whether you know it or not, you already are saving some of that amount in your Social Security account.While you can’t get at that money, as you can with most of your other savings, and Table 3.1 Required Saving Rates*

Years After Retirement

Years Before Retirement 10 15 20 25

15 32% 45% 56% 66%

20 22% 31% 39% 45%

25 16% 23% 29% 33%

30 13% 18% 22% 26%

35 10% 14% 17% 20%

40 8% 11% 14% 16%

*Assumptions: The real interest rate is 3% per year and salary keeps pace with inflation before retirement.

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A Safe Approach to Achieving Your Lifetime Financial Goals

the government can change the rules at any time, at present you can assume a significant amount of help.¹