Question

# Problem (5 marks) Daryl wishes to save money to provide for his retirement. He is now...

Problem

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?

(Please provide all the equation and step by step or Excel.xml in google drive )

(Please don't copy from another places, the answer will upload to Turnitin)

Solution :-

Today's Age = 30

Retirement Age = 64

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

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

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

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

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

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

= X * 5752.85 = \$799,176.70

X = \$138.918

Therefore Monthly Deposit = \$138.92

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