Question

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 $210,000 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 will leave the money in this fund until it is completely depleted when you are 80 years old.

LOADING...

​(Click the icon to view the present value annuity​ table.)                                            

LOADING...

​(Click the icon to view the future value annuity​ table.)

LOADING...

​(Click the icon to view the present value​ table.)                                                     

LOADING...

​(Click the icon to view the future value​ table.)

To make your plan work answer the following​ questions:

LOADING...

​(Click the icon to view the​ questions.)

1. How much money must you accumulate by​ retirement?

​(Hint​:

Find the present value of the

$210,000

​withdrawals.)

Calculate the present value to find out how much money must be accumulated by retirement. ​(Round your answer to the nearest whole​ dollar.)

The present value is $

.

More Informatiom

How much money must you accumulate by​ retirement? ​(Hint​: Find the present value of the $210,000 ​withdrawals.)
2.	How does this amount compare to the total amount you will draw out of the investment during​ retirement? How can these numbers be so​ different?
3.	How much must you pay into the investment each year for the first twentytwenty ​years? ​(Hint​: Your answer from Requirement 1 becomes the future value of this​ annuity.)
4.	How does the total​ out-of-pocket savings compare to the​ investment's value at the end of the twentytwenty​-year savings period and the withdrawals you will make during​ retirement?

PrintDone

Answer 1

1. Present Value of $210,000 = 210,000*PVIAF( 10%,40)

=210,000*9.7791

=$2,053,611

2. During your retirement years you will be able to withdraw 8,400,000(210,000*40 years) but at the age of 40 would have invested only $2,053,611. The money invested will continue to earn 10% interest.

3. Amount to be paid each year for 20 years = Future Value/ Future Value Factor

Future Value=$ 2,053,611

Future Value Factor= (10%,20)

Amount to be paid each year= 2,053,611/57.27 = 35,855.28

4. Total out of pocket savings = 2,053,611-(35855.28*20)

= $1,336,505.45