In Plato’s Republic, an old man is told by a younger friend, “I rather suspect that people generally think old age sits lightly upon your shoulders, not because of your cheerful disposition, but because you are rich.” Surely, wealth can be a great comforter during retirement. In addition to enjoying good health, two primary ingredients to a happy retirement are having sufficient income and having that income stream extend long enough to see you and your spouse through your latter years.

In our February column, we recommended planning conservatively, targeting your retirement income needs at 80 percent of your current take-home pay less Social Security benefits. (To obtain an estimate of your Social Security benefits, visit www.ssa.gov/sitemap.htm.) We also recommended that you project a long life expectancy (perhaps to 90 or beyond) and you include an adjustment for inflation (perhaps assuming three percent a year as a reasonable estimate).

Most retirement planning is based on the use of annuity calculations — similar to mortgages. When a bank grants you a mortgage, the bank is purchasing an annuity (stream of equal monthly payments) from you. In return for providing you with the loan, you agree to make the monthly payments for the duration of the mortgage.

Retirement planning is often based on your using your retirement savings (such as 401(k) and IRA accumulations) to purchase an annuity that will provide you and your spouse with incomes during your lifetimes. Often insurance companies become involved. In exchange for your retirement savings, they guarantee payments for as long as you or your spouse may live. They also may guarantee payments for a minimum of 20 years; therefore if you both die prematurely, your heirs will receive something. Such plans frequently factor in low rates of return on your money and do not provide for cost of living increases. Furthermore, if you live beyond the 20-year minimum guaranteed payment period, none of the funds used to purchase the annuity will remain for your heirs.

If you want higher returns on your retirement savings, while enjoying cost of living increases and the peace of mind that you can leave more to your heirs, consider using the following simple formula for an increasing perpetuity. A perpetuity is an annuity that lasts forever. An increasing perpetuity is one that provides for annual increases in your retirement income to compensate for inflation. An increasing perpetuity has the potential to provide increasing income during retirement and a larger estate for your heirs. Furthermore, the formula can be easily used to calculate how much you will need to fund your retirement. Here is how it works:

Accumulation = Annual Retirement Income/(Expected Return – Inflation Rate)

Suppose that in addition to Social Security, you want annual retirement income of $40,000 per year with 3 percent annual increases to cover inflation, and you anticipate being able to obtain an average annual rate of return on your retirement savings of 10 percent. You therefore would need to accumulate $40,000/(0.10 - 0.03) = $571,429 at retirement. If you invest the $571,429 and receive a 10 percent return, you will be able to draw $40,000 the first year, $41,200 the second, $42,436 the third, etc.

The information and planning ideas contained in this article are for general use only. Therefore, the ideas presented here should be relied upon only when coordinated with professional tax and planning advice.