Now let's look at things a little differently. Suppose that once you retire, you want to be able to withdraw $40,000 per year (starting one year from today) for a total of 20 years.

How much would you need to have in your account when you retire to make this work assuming an annual interest rate of 3.75%? 

 

How much would you need to have in your retirement account if you began these same 20 annual withdrawals immediately? 

 

 Let's assume that you want to have $1mm in your retirement account at the end of 30 years. You have now decided that you will deposit funds at the end of every month for 30 years. The interest rate is 3.75% per year. How much do you need to deposit each month?

 

 

Compare the results you got in part a for future value of a "regular" annuity compare these to the value you got for the annuity due. Now look compare the PV of the regular annuity in part to the PV of an annuity due.What is the relationship that? 

Using the time value of money concepts you have learned so far, why does this relationship (FV of regular annuity vs. annuity due and PV of regular annuity vs. annuity due) occur?