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 comma 000$210,000

per year for the next

4040

years​ (based on family​ history, you think​ you'll live to age

8080​).

You plan to save for retirement by making

2020

equal annual installments​ (from age

2020

to age​ 40) into a fairly risky investment fund that you expect will earn

1010​%

per year. You will leave the money in this fund until it is completely depleted when you are

8080

years old.

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

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

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

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

To make your plan work answer the following​ questions:

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

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

​(Hint​:

Find the present value of the

$ 210 comma 000$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 $

2,053,590

.

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?

Over the course of your retirement you will be withdrawing $		8,400,000	. However, by age 40 you only need to have invested
the present value.

These numbers are different​ because:

A.

You need to have far less accumulated than what you will withdraw because you only withdraw a portion of the investment every

yearlong dash—the

balance remains invested where it continues to earn

1010​%

interest.

B.

You need to have the same accumulated as you will withdraw because you will not earn further interest on your investment when you reach retirement.

C.

You need to have far more accumulated than what you will withdraw because you will withdraw a large portion of the investment every

yearlong dash—the

balance remains invested where it continues to earn

1010​%

interest.

D.

None of the above.

Please not sure of it is A , B Oor D . THANKS

Answer 1

First we need to calculate the P of all the withdraw that you intend to make after retirement

Present value of annuity is the present worth of cash flows that is to be received in the future, if future value is known, rate of interest in r and time is n then PV of annuity is

PV of annuity = P[1- (1+ r)^-n]/ r

= 210000[1- (1+ 0.1)^-40]/ 0.1

= 210000[1- (1.1)^-40]/ 0.1

= 210000[1- 0.0220949281521799]/ 0.1

= 210000[0.97790507184782/ 0.1]

= 210000[9.7790507184782]

= 2053600.65

That amount is equal to the FV of all the deposit that you will make

FV = Annual deposit * FV of annuity @ 10% n = 20 years

2053600.65 = Annual deposit * 57.275

Annual deposit = 2053600.65/57.275

                            = 35855.1

You need to deposit $35855.1 per year in the account

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