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 $ 220,000 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 15 equal annual installments​ (from age 25 to age​ 40) into a fairly risky investment fund that you expect will earn 12% per year. You will leave the money in this fund until it is completely depleted when you are 80 years old.

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

​(Hint​:Find the present value of the $ 220,000 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. 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 $			. However, by age 40 you only need to have invested

These numbers are different​ because:

A.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 12% 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 less accumulated than what you will withdraw because you only withdraw a portion of the investment every yearlong dashthe balance remains invested where it continues to earn 12​% interest.

D.None of the above.

3. How much must you pay into the investment each year for the first fifteen ​years?​(Hint​: Your answer from Requirement 1 becomes the future value of this​ annuity.) ​(Round your answer to the nearest whole​ dollar.)

You must pay $

into the investment each year for the first fifteen years.

4. How does the total​ out-of-pocket savings compare to the​ investment's value at the end of the fifteen-year savings period and the withdrawals you will make during​ retirement?​ (Use the investment rounded to the nearest whole number that you calculated​ above, then round your final answer to the nearest whole​ dollar.)

The total out-of-pocket savings amounts to $				. This is far		than the investment's worth at the end
of fifteen years and remarkably		than the amount of money you will eventually withdraw from the investment.

Answer 1

Part 1)

The present value can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The formula/function for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate, Nper = Period, PMT = Payment and FV = Future Value.

Here, Rate = 12%, Nper = 40, PMT = $220,000 and FV = 0

Using these values in the above function/formula for PV, we get,

Present Value = PV(12%,40,220000,0) = $1,813,631

The present value is $1,813,631.

_____

Part 2)

Over the course of your retirement you will be withdrawing $8,800,000 (220,000*40). However, by age 40 you only need to have invested $1,813,631 (the present value).

_____

These numbers are different​ because:

You need to have far less accumulated than what you will withdraw because you only withdraw a portion of the investment every yearlong the balance 88% remains invested where it continues to earn 12​% interest. (which is Option C) [the answer is self-explanatory]

_____

Part 3)

The amount to be paid into the investment each year for the first fifteen ​years can be derived with the use of PMT (Payment) function/formula of EXCEL/Financial Calculator. The function/formula for PMT is PMT(Rate,Nper,PV,FV) where Rate = Interest Rate, Nper = Period, PV = Present Value and FV = Future Value.

Here, Rate = 12%, Nper = 15, PV = 0 and FV = $1,813,631

Using these values in the above function/formula for PMT, we get,

Amount to Paid into Investment Each Year = PMT(12%,15,0,1813631) = $48,649

You must pay $48,649 into the investment each year for the first fifteen years.

_____

Part 4)

The total out-of-pocket savings amount to $729,739 (48,649*15). This is far lesser than the investment's worth at the end of fifteen years and remarkably lower than the amount of money you will eventually withdraw from the investment.

_____

Notes:

The answer to Part 4) blanks may vary in terms of words (lesser/lower).