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 If she earns 8% on her savings not withdrawn, how much should her first withdrawal be?

please show work! Thank you

Answer 1

Formula for Present value of growing annuity can be used to compute first payment as:

PV = P/(r-g) x [1-{(1+g)/ (1+r)} ⁿ]

P = PV x (r-g) / [1-{(1+g)/ (1+r)} ⁿ]

PV = Present value of annuity = $ 50,000

P = First payment

r = Rate per period = 8 % or 0.08

g = Growth rate = 6 % or 0.06

n = Number of periods = 10

P = $ 50,000 x (0.08-0.06)/ [1-{(1+0.06)/ (1+0.08)} ¹⁰]

P = ($ 50,000 x 0.02)/ [1-{(1+0.06)/ (1+0.08)} ¹⁰]

P = $1,000/ [1-{(1.06)/ (1.08)} ¹⁰]

P = $1,000/ [1-(0.981481481481)¹⁰]

P = $1,000/ (1- 0.829508991190107)

P = $1,000/ 0.170491008809893

P = $ 5,865.411947 or $ 5,865.41

First withdrawal of Suzie will be $ 5,865.41