Question

D Week5 O Do Spru 2018-SE2-ACCT640.30365 Homework: Week 5 Score: 0 of 12 pts P12-60B (similar to) zach jones & 18/5/18 6:00 PM 5 of 5 (0 complete) HW Score: 0%, 0 of 60p You are planning for a very early retirement You would like to retire at age 40 and have enough money saved to be able to draw $230,000 per year for the next 40 years (based on family history, you think you'll live to age 80) You plan to save for retirement by making 20 equal annual installments (from age 20 to age 40) into a fairly risky investment fund that you expect will earn 10% per year You wil leave the money in this fund until it s completely depleted when you are 80 years old Click the icon to view the present value annuity table) (Cick the icon to view the future value annuity table ) (Click the icon to view the present value table ) Click the icon to view the future value table) 1. How much money must you accumulate by retirement? (Hint Find the present value of the $230000 withdrawas ) t lated by retirement (Round your answor to the nearest whole dollar)

Answer 1

1. Money to be accumulated at retirement = Annuity x PVA_{10%, n=40} = $ 230,000 x 9.779 = $ 2,249,170.

2. Total amount to be drawn out during retirement = $ 230,000 x 40 = $ 9,200,000.

Money to be accumulated at retirement is far less. The difference can be explained by the amount of interest earned at 10% over the period of 40 years.

3. Future value of annuity A at 10% = $ 2,249,170. = Annuity x FVA_{10%, n=20}

or Annuity x 57.275 = $ 2,249,170

Annuity = $ 39,269.66 or $ 39,270

Therefore, the amount that is to be invested for the first 20 years = $ 39,270 per year.

4. Total out-of-pocket investments = $ 39,270 x 20 = $ 785,400.

This is far less than the amount accumulated at the end of 20 years.