Retirement Calculator

The projection combines two standard time-value formulas. The lump-sum term, PV times (1 + r/12) raised to 12t, grows what you already have; the annuity term multiplies the monthly contribution by [(1 + r/12) to the 12t, minus 1] divided by r/12, which is the accumulated value of a stream of equal deposits. Monthly compounding is used because contributions arrive monthly, and the two terms are additive because compound growth is linear in the starting balance. The 7 percent default return reflects long-run nominal equity performance; the 3 percent inflation input then deflates the result by (1 + i) to the t, converting future dollars into today's purchasing power. That distinction matters enormously: at 3 percent inflation, a dollar in 35 years buys about 36 cents of what it buys now. The income figure applies the 4 percent rule, withdrawing 4 percent of the balance in year one. Its main limitations are structural rather than arithmetic. A single constant return assumes away sequence-of-returns risk, where a poor first decade of retirement damages a portfolio far more than the same returns arriving later. The model also ignores taxes, Social Security, employer matching, contribution-limit ceilings and any change in savings rate over a career, so it is best read as a sensitivity tool - vary the return between 5 and 8 percent to see the plausible spread rather than treating one output as a forecast.

Retirement planning shifted from an employer problem to an individual one over roughly two decades. The Employee Retirement Income Security Act of 1974 set funding standards for traditional defined-benefit pensions and simultaneously created the individual retirement account. Four years later, the Revenue Act of 1978 added section 401(k) to the tax code; the benefits consultant Ted Benna read the provision in 1980 as permitting salary deferrals with an employer match and set up an early plan in 1981, after which the IRS issued proposed regulations and adoption spread rapidly. The consequence was that projecting a personal balance, rather than reading a promised pension formula, became the central planning exercise. The withdrawal side was quantified later. William Bengen, a financial planner in California, published Determining Withdrawal Rates Using Historical Data in the Journal of Financial Planning in October 1994, testing withdrawal rates against historical US market returns and finding that about 4 percent, inflation-adjusted, survived every 30-year period he examined. Philip Cooley, Carl Hubbard and Daniel Walz of Trinity University extended the analysis in 1998 with portfolio-success tables across stock and bond mixes, work widely known as the Trinity study. Together these two papers gave the 4 percent rule the empirical footing that keeps it in general use.