Retirement Calculations - Prof. Richard B. Goldstein

How Much Does One Need to Save for Retirement?

Formula Derivations and Examples
Future Value: FV = pS(e^rt - e^gt)/(r - g)
where p = percentage saved, S = salary, r = rate of growth of investments,
g = growth rate of salary, and t = number of years until retirement.

C = current amount saved for retirement

Final Salary FS = Se^gt
Future Total Value FT = FV + FC where FC = Ce^rt

To achieve a yearly income of q% of final salary one needs to save
[qSe^gt(1 - e^{(g -
r)L}) - C(r-g)e^rt]/S[e^rt - e^gt] where L = years of life expectancy.

S = Current Salary ($)
r = Annual Growth Rate of Investments (%)
g = Growth Rate of Salary (%)
t = Number of Years until Retirement
p = Percent of Salary Saved (%)
C = current amount saved for retirement ($)
L = Life Expectancy (years in retirement)
q = Percent of Final Salary needed for Retirement

FS = Future Salary at Retirement ($)
FV = Future Value of Annuity ($)
FC = Future Value of Current Savings ($)
FT = Total Value of Retirement ($)
YI = Starting Yearly Income in Retirement ($)
Starting salary as a percentage of final salary (%)
Percent of Salary that needs to be Saved

How much can one Spend in Retirement and for how long?

Formula Derivations and Examples
Yearly Withdrawal W = (r - g)*PV/(1 - e^{(g - r)L}) where r = rate of growth of investments,
g = growth rate of income or inflation, PV = present value of retirement nest egg, and
L = number of years retirement money should last or life expectancy
L = ln[1 - (r - g)(PV/W)]/(g - r)

How much?

For how long?

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