SOLUTION: Julie won $200 000 in a lottery! She estimates that to live comfortably she will need to withdraw $5000 per month for the next 50 years. Her savings Account earns 4.25%, compounded

Question 1148193: Julie won $200 000 in a lottery! She estimates that to live comfortably she will need to withdraw $5000 per month for the next 50 years. Her savings Account earns 4.25%, compounded monthly. Can Julie afford to retire and live off her lottery winnings?
Found 3 solutions by josmiceli, ikleyn, MathTherapy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!

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She will end up with $1,668,304.65, but she needs

$3,000,000, so she can't live off the winnings
Get a 2nd opinion if needed

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

Estimations in the post by @josmiceli are very crude, but they produce the correct NEGATIVE answer.

It is possible to provide more accurate estimations, but they will not change this negative answer.

Again, the estimations by @josmiceli are correct, and the ANSWER is negative:

Julie CAN NOT afford to retire and live off her lottery winnings.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Julie won $200 000 in a lottery! She estimates that to live comfortably she will need to withdraw $5000 per month for the next 50 years. Her savings Account earns 4.25%, compounded monthly. Can Julie afford to retire and live off her lottery winnings?

You don't need to calculate how much she needs for 50 years or 600 (50 * 12) months.
Common sense should DICTATE that about 40 payments of $5,000 each, will DEPLETE these funds entirely, because 40($5,000) = $200,000.
So, right away, you see that it's impossible for this amount to last anywhere close to 600 months or for her to get 600 payments
when it's ALMOST finished after she receives 40 payments (40 months) of $5,000 each.
Another way to look at this: Withdrawing $5,000 per month, for just 1 year (12 months) will deplete the funds by at least $60,000 (5,000 * 12).
How much longer than a year do you think this amount would last?
NOT REQUIRED, but what the HECK!!
As a matter of fact, for her to be able to withdraw $5,000 per month for 50 years (600 months), she'll need to have $1,242,519.27, at the beginning of her retirement, or year 0.
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