Question

You just decided to begin saving for retirement. You will make deposits of $1,000 per month into a retirement account that earns 8.00% p.a. The first deposit is made today and the last deposit will be made when you retire exactly 30 years from today. (Note: you make 361 total monthly deposits into your retirement account.) You will begin to make withdrawals from the account the first month after you retire. If you plan to live an additional 25 years and leave $900,000 to your heirs, you will be able to withdraw $_____ each month. (Note: you make 300 total monthly withdrawals from your retirement account.)

Answer 1

Monthly withdraw= $4,752.01

Step-by-step explanation:

Giving the following information:

Monthly deposit= $1,000

Number of perios= 361 months

Interest rate= 0.08/12= 0.0067

First, we need to calculate the Future Value at the moment of retirement:

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit

FV= {1,000*[(1.0067^361) - 1]} / 0.0067

FV= $1,513,584.37

Now, we can calculate the monthly withdraw:

PV= 1,513,584.37 - 900,000= $613,584.27

Monthly withdraw= (FV*i) / [1 - (1+i)^(-n)]

Monthly withdraw= (613,584.37*0.0067) / [1 - (1.0067^-300)]

Monthly withdraw= $4,752.01