Question

P 4-42 (similar to Question Help You have just turned 22 years old, received your bachelors degree, and accepted your first job. Now you must decide how much money to put into your retirement plan. The plan works as follows: Every dollar in the plan eams 7.1% per year. You cannot make withdrawals until you retire on your 65th birthday. After that, you can make withdrawals as you see fit You decide that you wil plan to Ive to 100 and work until you tum 65. You estimate that to live comfortably in retirement, you will need $100,000 per year, starting at the end of the first year of retirement and ending on your 100th birthday. You will contribute the same amount to the plan at the end of every year that you work. How much do you need to contribute each year to fund your retirement? Your annual contribution should beS(Round to the nearest cent.)

Answer 1

Fund size needed at the time of retirement can be computed using formula for Present value of annuity as:

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

P = Periodic cash flow = $ 100,000

r = Rate per period = 7.1 % or 0.071 p.a.

n = Numbers of periods = 100 – 65 = 35 periods

PV = $ 100,000 x [1-(1+0.071)^-35/0.071]

     = $ 100,000 x [1-(1.071)^-35/0.071]

     = $ 100,000 x [(1-0.09065014871)/0.071]

     = $ 100,000 x (0.90934985129/0.071)

     = $ 100,000 x 12.8077443844

    = $ 1,280,774.43843651 or $ 1,280,774.44

$ 1,280,774.44 is the future value of deposited annuity which can be computed using formula for future value of annuity as:

FV = P x [(1+r) ⁿ – 1/r]

P = FV/ [(1+r) ⁿ – 1/r]

FV = Future value of the deposits = $ 1,280,774.44

P = Periodic cash flow

r = Rate per period = 7.1 % or 0.071 p.a.

n = Numbers of periods = 65 – 22 = 43 periods

P = $ 1,280,774.44 / [(1+0.071)⁴³ – 1/0.071]

     = $ 1,280,774.44 / [(1.071)⁴³ – 1/0.071]

     = $ 1,280,774.44 / [(19.096212806719 – 1)/0.071]

    = $ 1,280,774.44 / (18.096212806719/0.071)

    = $ 1,280,774.44 / 254.87623671435

   = $ 5,025.08

Annual contribution should be $ 5,025.08

Answer 2

You have just turned 22 years old, received your bachelor's degree and accepted your first job. Now you must decide how much money to put into your retirement plan. The plan works as follows: Every dollar in the plan earnss 7% per year. You cannot make withdrawals until you retire on your 65th birthday. After that, you can make withdrawals as you see fit. You decide that you will plan to live to 100 and work until you turn 65. You estimate that to live comfortably in retirement, you will need $100,000 per year, starting at the end of the first year of retirement and ending on your 100th birthday. You will contribute the same amount to the plan at the end of every year that you work. How much do you need to contribute each year to fund your retirement given a 3% inflation rate?