You would like to have $1,000,000 in savings as of the day you retire exactly 40

Question

You would like to have $1,000,000 in savings as of the day you retire exactly 40 years from now. Beginning one year from today, you plan to deposit an equal amount in a mutual fund each year, with the last payment 40 years from today. (You will make 40 deposits.) (a) If you think the fund will earn a 6% return per year, what do you need to save each year to reach your goal? (b) What do you need to save each year if you think the fund will earn 5% a year? (c) Suppose you decide to start your savings ten years later (i.e., instead of making your first deposit one year from now, you

Explanation / Answer

PLEASE RATE ME AND AWARD ME KARMA POINTS IF IT IS HELPFUL FOR YOU The reality, however, is probably somewhere in between. The problem with the picture is that the pleasure and comfort of your later years depend, to an ever-increasing degree, on the actions you take today. So many changing facets of the American workplace have made it more important than ever to take control of your financial future. By investing now with a long-term focus, you can greatly improve your chances of having a fulfilling retirement. Americans used to count on a pension plus Social Security to get them through those "golden years." These days, people change jobs more often, rely on dual incomes, and manage their own retirement funds through defined contribution plans. By most estimates, you'll need between 60% and 100% of your final working years' income to maintain your lifestyle after retiring. Sources of Retirement Income This chart represents a breakdown of income sources for all retirees (aged 65 and over). Source: Social Security Administration, 2010 (using 2008 data, most recent available). Saving Is the Key Component of Retirement Income The accompanying pie chart shows the importance of saving now toward a retirement fund. Not only are Social Security benefits less significant, but the sums are diminishing and the age at which you can begin to receive benefits is higher. You can contact Social Security at 1-800-772-1213 to learn what you can expect in benefits, and when. Benefits are calculated on your earnings, with certain variable factors. Alas, the responsibility for the bulk of your nest egg rests with you. Social Security represents approximately 36% of the aggregate income of Americans aged 65 and older, according to the Social Security Administration. Also, as you begin thinking about how much you'll need for a comfortable retirement, you may be startled to learn the impact of inflation. At an average inflation rate of 3%, your cost of living would double every 24 years. Your annual income will need to increase each year even during retirement in order to keep up with the gradual rise in prices of everyday goods. You'll also have to consider the likelihood of increased medical costs and health insurance as you grow older. The average nursing home stay, for instance, now costs more than $83,000 a year and could rise to over $150,000 per year by 2030, assuming an annual inflation rate of 3%.1 Meeting Your Goals Now that you have an idea how much you'll need to finance your retirement years, of which there can easily be 25 or more, you may better understand the urgency to build your assets. How Much Do You Need to Retire in Style? Financial experts estimate that most of us will need about 60% to 100% of our annual preretirement income to live on each year after we retire. Find out how close you are to meeting this goal by completing the exercise below. Estimate your last working year's salary. Multiply your current salary by the inflation factor from the table below, based on the number of years you have until retirement. This represents the future value of your salary, assuming 3% annual inflation. Example: If you are currently making $40,000 and have 20 years until retirement, your formula is $40,000 x 1.81 = $72,400 Determine what percentage of your current income you expect to need after retirement. If 100% seems high, consider that while you may be able to stop paying some expenses, like mortgage payments, other expenses will likely increase, such as health and travel expenses. Multiply that percentage by the amount in #1. Example: $72,400 x .80 = $57,920 Estimate your future Social Security and retirement benefits. The best source for Social Security benefit projections is your annual Social Security statement (or one of the calculators from www.ssa.gov). If you don't have that, you can get a very rough estimate of your benefit from Table 2 below. If you have your Social Security Benefit Statement, multiply the monthly amount listed under "If you continue working until full retirement age" by 12, then multiply that figure by the inflation factor from Table 1 below. Example: If your benefit statement shows an estimated monthly benefit of $1,153, your formula is $1,153 x 12 x 1.81 = $25,043 If you are using Table 2, take the number corresponding to your annual salary and years to retirement. Example: If you currently earn $40,000 and have 20 years to retirement, your estimated benefit would be $25,000 Subtract your Social Security benefits and other retirement benefits from the annual amount calculated in #1. This will give you an estimate of how much of your own savings you will have to use each year in retirement. Example: $57,920 - $25,000 = $32,920 Estimate the total amount that you will have to put aside in retirement accounts such as 401(k) plans, IRAs, and personal savings. To determine how much you will need to save, multiply 19.3 by the annual amount you calculated in #3. This multiplier represents how much savings you would need to last 28 years at 3% inflation and earning a 6% annual return. A healthy, 65-year old male has a 10% chance of living longer than 28 years. Example: $32,920 x 19.3 = $635,356 Enter the amount of your current savings and investments and multiply it by the growth factor from the accompanying table. This is what your savings would be worth by the time you reach retirement, assuming an 8% return compounded annually. Example: $30,000 x 4.66 = $139,800 If line 5 is larger than line 4, congratulations! You are on your way to meeting your retirement goal. Keep saving! If line 4 is larger than line 5, subtract line 5 from line 4. Enter that amount here. This is the additional amount you'll need. Example: $635,356 - $139,800 = $495,556 Divide #6 by the multiplier in the table below for the number of years until your retirement. The multiplier represents how large your savings will grow based on your annual contribution, assuming an 8% annual return. The result is the approximate amount you may want to set aside each year. Example: $495,556 ÷ 49.42 = $10,027 Table 1 - Factors* Years Inflation Growth Multiplier 5 1.16 1.47 6.34 10 1.34 2.16 15.65 15 1.56 3.17 29.32 20 1.81 4.66 49.42 25 2.09 6.85 78.95 30 2.43 10.06 122.35 35 2.81 14.79 186.10 40 3.26 21.72 279.78 Table 2 - Social Security Income Years to Retirement Current Salary 40 35 30 25 20 15 10 5 $20,000 29,500 27,000 25,000 22,500 20,500 19,000 17,500 16,000 30,000 32,500 30,000 27,500 25,000 22,500 21,000 19,000 17,500 40,000 35,500 32,500 30,000 27,000 25,000 23,000 21,000 19,000 50,000 38,500 35,500 32,500 29,500 27,000 25,000 22,500 21,000 60,000 41,500 38,000 35,000 32,000 29,000 26,500 24,500 22,500 70,000 44,500 41,000 37,500 34,000 31,000 28,500 26,000 24,000 80,000 47,500 43,500 40,000 36,500 33,500 30,500 28,000 25,500 90,000 50,500 46,500 42,500 39,000 35,500 32,500 29,500 27,500 97,500 + 53,000 48,500 44,500 40,500 37,000 34,000 31,000 28,500 *Assumes 3% annual inflation and a 5% annual return. Pensions, Social Security, and Other Allies Traditional pensions (private and government) are estimated to supply about 17% of the aggregate income of today's retirees, while Social Security is estimated to supply 36%, although nearly two-thirds of retirees rely on Social Security for 50% or more of their income, according to the Social Security Administration (2010; using 2008 data, most recent available). Still, you'll probably fall far short of your goal. A radically reduced standard of living for a quarter century or more is hardly the stuff "golden age" dreams are made of. Fortunately, you have some allies. First is the power of compounding, which takes advantage of time. Tax deferral is another ally. Using investment vehicles such as 401(k) plans or individual retirement accounts (IRAs), you can put off paying taxes on your earnings until you are retired and potentially in a lower tax bracket. Meanwhile, your contributions may be pretax or tax deductible, helping reduce current tax bills. For example, an investment of $10,000 would grow to more than $100,000 after 30 years, at an annual return of 8%, if all the returns were reinvested and the account grew tax deferred. As with all hypotheticals, this example does not represent the performance of any specific investment and the earnings would be s

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