Question

Your aunt Suzie expects to live another 10 years. (Should she live longer, you are expected to provide for her.). She currently has $50,000 in savings which she wishes to spread evenly in terms of purchasing power over the remainder of her life. Since she feels inflation will average 6% annually, her annual beginning-of-year withdrawals should increase at a 6% growth rate. If she earns 8% on her savings not withdrawn, how much should her first withdrawal be?

Answer 1

$50000 is the PV of a growing annuity due, the growth rate
being the inflation rate of 6%.
The PV of growing annuity =(1+r)*(( P/(r-g))*[1-((1+g)/(1+r))^n
where P = first payment, r = rate of interest per period,
g = growth rate and n = number of periods.
Substituting values we have
50000 = (1.08)*((P/(0.08-0.06))*((1-((1.06/1.08)^10)))) =
Solving for P (the first payment)
P = 50000*((0.08-0.06))/(((1-((1.06/1.08)^10))*1.08))) =	$ 5,430.94