Question

Daryl wishes to save money to provide for his retirement. He is now 30 years old and will be
retiring at age 64. Beginning one month from now, he will begin depositing a fixed amount into
a retirement savings account that will earn 12% compounded monthly. Then one year after
making his final deposit, he will withdraw $100,000 annually for 25 years. In addition, and after
he passes away (assuming he lives 25 years after retirement) he wishes to leave in the fund a sum
worth $1,000,000 to his nephew who is under his charge. The fund will continue to earn 12%
compounded monthly. How much should the monthly deposits be for his retirement plan?

Answer 1

Answer:

The answer is $138.92

Explanation:

Solution

Given that:

Daryl today's Age = 30

The Retirement Age = 64

The Total Monthly Deposits = ( 64 - 30 ) * 12 = 408

Now,

In case of 12% Compounded Monthly , Interest Rate per month = ( 12% / 12 ) = 1%

Then,

The Effective Interest Rate per year = ( 1 + 0.12/12 )12 - 1 = 1.1268 - 1 = 0.1268 = 12.68%

So,

The Present value of Annual 25 Years withdrawal of $100,000 at time of Retirement = $100,000 * PVAF ( 12.68% , 25 )

= $100,000 * 7.4864

= $748,642.20

The Present Value of Money for nephew at time of Retirement = $1,000,000 * PVF ( 12.68% , 25 )

= $1,000,000 * 0.050535

= $50,534.52

Now

The Present Value of total Amount Required at time of Retirement = $748,642.20 + $50,534.52

= $799,176.70

Now

The monthly deposit be X

Which is,

= X * FVAF ( 408 , 1% ) = $799,176.70

= X * 5752.85 = $799,176.70

X = $138.918

Therefore, Monthly Deposit  for his retirement plan is = $138.92