Question

You will save $7,000 per year for the next 30 years. You will earn 10% on your savings. At the end of 30 years, you will retire, and you expect to live for 40 years after that. How much can you withdraw every year for 40 years and not run out of money? Round your answer to the nearest whole number, for example 400

Answer 1

Formula for FV of annuity can be used to compute future fund size in 30 year as:

FV = P x [(1+r) ⁿ – 1/r]

P = Periodic cash flow = $ 7,000

r = Rate per period = 10 % or 10/100 = 0.1 p.a.

n = Numbers of periods = 30

FV = $ 7,000 x [(1+0.1)³⁰ – 1/0.1]

     = $ 7,000 x [(1.1)³⁰ – 1/0.1]

     = $ 7,000 x [(17.449402268886 – 1/0.1]

     = $ 7,000 x (16.449402268886/0.1)

     = $ 7,000 x 164.49402268886

     = $ 1,151,458.15882205 or $ 1,151,458.16

This fund of $ 1,151,458.16 will facilitate cash flow for 40 years retirement life. Annual cash withdrawal during retirement can be computed using formula for PV of annuity as:

PV = P x [1-(1+r)^-n/r]

P = PV/ [1-(1+r)^-n/r]

P = Periodic cash flow

r = Rate per period = 10 % or 10/100 = 0.1 p.a.

n = Numbers of periods = 40

P = $ 1,151,458.16 / [1-(1+0.1)^-40/0.1]

   = $ 1,151,458.16 / [1-(1.1)^-40/0.1]

= $ 1,151,458.16 / [(1-0.02209492815)/0.1]

   = $ 1,151,458.16 / (0.97790507185/0.1)

   = $ 1,151,458.16 / 9.7790507185

= $ 117,747.43704379 or $ 117,747.44

Annual withdrawal will be $ 117,747.44 for 40 years.