Question

You are planning to retire in 40 years. You currently have $ 300,000 in a bond mutual fund and $100,000 in a stock mutual fund. You plan to invest $10,000 per year in the stock mutual fund for the next 40 years (i.e., from t=1 to t=40). The bond fund is expected to earn 4% per year, compounded annually, and the stock account is expected to earn 9% per year, compounded annually, indefinitely. When you retire in 40 years, you plan to transfer your money from both accounts to an IRA account that will earn 6% per year, compounded annually. Upon retirement, you plan to withdraw an equal amount of money for each of next 20 years (i.e., t=41 to t=60), so that there will be nothing left in the account at the end of t=60. How much can you withdraw each year? Please be specific.

What would you answer be if you plan to bequest (or leave) $ 5 million to your children at the end of t=60?

Answer 1

Step 1 - CAlculate the Future Value of all the investments:

a) $300000 in Bond Mutual fund, Fv after 40 years, Rate 4%

FV = 300000(1.04)⁴⁰

= 300000 x 4.801021

= 1440306.188

b) $100000 in Stock mutual fund, Fv after 40 years @ 9%

= 100000 (1.09)⁴⁰

= 100000 x 31.409420

= 3140942.005

c) $10000 per year for next 40 years, Rate 9%

= 10000 x cumulative annuity factor @9% for 40 years

or Solve it with Texas Ba 2 calculator as . Put values as N=40,I/Y=9, PV=0, PMT = 10000

compute FV = 3378824.450

Step 2

Calculate the accumulated balance you will have after 40 years

1440306.188 + 3140942.005 + 3378824.450

= 7960072.643

Step 3

Now you want annual payent to exaust the total amount fully in next 20 years rate 6%

The above accumlated amount becomes your Present value T40. So calculate annual withdrawls

PV = Annual Payments x cumulative discounting factor @ 6% for 20 Years.

7960072.643 = AP x 11.4699

Annual WIthdrawls = 7960072.643 / 11.4699 = 693996.69

Seperate Situation = Plan to leave $5000000 for your child

Calculate PV of 5000000 at 6% 20 year period.

= 5000000 / (1.06)²⁰

= 1559023.634

Dedut this amount from 7960072.643 and again calculate the annual withdrawl.

7960072.643 - 1559023.634 = 6401049

6401049.009 = AP x 11.4699

= AP = 6401049.009 / 11.4699

Annual Withdrawls= 558073.65