Question

Problem 4. You would like to have enough money saved to receive $200,000 per year after retirement so that you and your family can lead a good life for 30 years (from age 65 to 95). You will make your first withdraw of $200,000 at the end of year when you are 65. If you will be 35 years old when you graduate and plan on making savings contributions at the end of your first year out of school, how much would you need to save in your post-MBA retirement fund to achieve this goal? Assume an interest rate is 8%.  

Answer 1

Formula for PV of annuity can be used to compute the size of fund needed at the time of retirement to facilitate cash outflow of $ 200,000 per years as:

PV = P x [1-(1+r)^-n/r]      

P = Periodic cash flow = $ 200,000

r = Rate per period = 8 % or 0.08 p.a.

n = Numbers of periods = 95 – 65 = 30

PV = $ 200,000 x [1-(1+0.08)^-30/0.08]

     = $ 200,000 x [1-(1.08)^-30/0.08]

    = $ 200,000 x [(1-0.09937733)/0.08]

    = $ 200,000 x (0.90062267)/0.08)

    = $ 200,000 x 11.2577833

    = $ 2,251,556.67

$ 2,251,556.67 is the future value of all annual contributions made in post retirement fund.

Annual contribution for this fund can be computed using formula for FV of annuity as:

FV = C x [(1+r) ⁿ – 1/r]

C = FV/[(1+r) ⁿ – 1/r]

C = Periodic cash flow

r = Rate per period = 8 % or 0.08 p.a.

n = Numbers of periods = 65 – 35 = 30

C = $ 2,251,556.67/ [(1+0.08)³⁰ – 1/0.08]

    = $ 2,251,556.67/ [(1.08)³⁰ – 1/0.08]

    = $ 2,251,556.67/ [(10.06265689 – 1)/0.08]

    = $ 2,251,556.67/ (9.06265689/0.08)

    = $ 2,251,556.67/113.2832111

   = $ 19,875.47

$ 19,875.47 of annual contribution needed in the retirement fund to achieve the goal.