Question

Seeing multiple answers to the same question...

Please give detailed solution with right answer without excel. An explanation would be great.

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

Given:

Current age 30

Retirement age: 64

Amount to be deposited one month from now: X

Interest: 12% compounded monthly

After one year from retirement annual withdrawal: 100,000 for 25 years

Amount available after 25 years after retirement: 1,000,000

Post retirement interest rate: 12% compounded monthly

Solution:

The first step will be to find the sum that will be required at the end of retirement. This is nothing but:

100,000PVIFAi%,25 years + (1,000,000/((1+i)^25)

Since i is compounded monthly, we have to find the effective interest rate. This can be done as under:

Annual interest: 12%

Monthly interest: 12%/12 = 1%

Effective interest is: [(1.01)^12]-1 or 12.6825%

Now using the effective interest rate in the above formula the value at the end of retirement is:

100,000PVIFA12.6825%%,25 years + [1,000,000/((1.126825)^25)]

Where PVIFA is given by:

(100,000/0.126825)*[1-{1/(1.126825^25)}] = 748,642

1,000,000/((1.126825)^25) = 50,534

Therefore the present value of the cash flows is 748,642+50,534 = 799,177.

This is the amount required when Darul reaches 64. This can be achieved as under

Monthly investment amount: X

Interest (monthly): 12%/12 = 1%

Number of payments to be made: (64-30)*12 = 296

Therefore the amount to be invested is:

XFVIFA1%,296 = 799,177, where FVIFA is given as:

X/.01*[(1.01^296)-1] = 799,177

X=443.58.

The amount to be save every month is therefore USD 443.58.