## The Retirement Investment and Income Simulation Spreadsheets

Tom O'Haver, University of Maryland

These Excel 5.0 spreadsheet simulations were developed for instructional purposes, to demonstrate in a graphic and interactive manner the potential benifits of long-term investing. They are not intended as tools for detailed personal financial planning.

The Investment Simulation Spreadsheet is a simulation of saving and investing for retirement. It shows how much you can accumulate in a tax-deferred retirement account (e.g. an IRA or 401k account) over a 35-year period by saving a certain amount each year and investing it in a combination of fixed-interest or variable (equity) instruments.

The Income Simulation Spreadsheet shows how much income you can withdraw from a retirement account (e.g. an IRA or 401k account) that is invested it in a combination of fixed-interest or variable (equity) instruments.

Both of the simulations use a random-number generator to simulate the fluctuation (volatility) in the investment returns of equities (stocks and stock mutual funds). Most spreadsheets have only a uniformly-distributed random number function (RAND) and not a normally-distributed random number function like a haystack curve, but it's much more realistic to simulate deviations that are normally distributed, because normal distributions have more small deviations that are close to the mean and few deviations that are far from the mean. In terms of investments, small losses and gains are much more common that large ones. So these spreadsheets make use of the Central Limit Theorem to create approximately normally distributed random numbers by combining several RAND functions. For example, the expression sqrt(3)*(RAND()-RAND()+RAND()-RAND()) creates nearly normal random numbers with a mean of zero, a standard deviation very close to 1, and a maximum range of ±4. (With 6 RAND functions, the formulation works similarly, but has a larger maximum range: sqrt(2)*(RAND(size(x))-RAND(size(x))+RAND(size(x))-RAND(size(x))+RAND(size(x))-RAND(size(x)))).

(c) 1997, 2017 T. C. O'Haver, The University of Maryland at College Park
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