You are trying to plan for retirement in 10 years and ...



You are trying to plan for retirement in 10 years and currently you have $150,000 in a savings account and $250,000 in stocks. In addition, you plan to add to your savings by depositing $10,000 per years in your savings account at the end of each of the next 10 years until retirement.   

a. assuming your account returns 12% compounded annually, how much will you at the end of 10 years.

The $10,000 that would be deposited annually represents an annuity, to calculate the FV of the annuity 10 years from now:

[pic][pic]

[pic]

= $175,487.35

The future value of the $150,000 can be calculated using the following formula:

[pic]

= [pic]

= $465,877.23

FV of the amount invested in stocks (Assuming the return on stocks is also 12%)

= [pic]

= $776,462.05

Therefore at the end of 10 years, I would have:

$175,487.35 + $465,877.23 + $776,462.05

=$1,417,826.63

= $1,417,827 (Rounded to the nearest whole dollar)

b. If you expect to live 20 years after you retire, and at retirement, you deposit all your savings in a bank account paying 11%, how much can you withdraw each year after retirement (20 equal withdrawals beginning 1 year after you retire) to end up with a zero-balance at death?

The amount that you can withdraw for 20 years would represent an annuity, and since at death the balance would be $0, and we know that the PV of this annuity is $1,417,826.63

Therefore:

[pic]

$1,417,826.63 = 7.96333C

C = [pic]

= $178,044

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