Mr. X plans to retire exactly twenty years from now and he would like to have accumulated, by retirement, enough money to enjoy a $100,000 per year retirement income beginning in year 21 and continuing in perpetuity thereafter. So far he has saved up $500,000, all in stocks (that is, his pension account contains $50,000).

a) What must his annual contributions be if he is to achieve his goal (assume he makes 20 payments)? He expecs to earn 10% on his money.

b) The stock market collapses. By the end of the day his accumulated wealth has fallen to $30,000. Assuming he still expects to earn 10%, how much must he now contribute(assume 20 equal payments)?

for a I got -13,686.03 is it correct?

please help me some one!

Akhatoon, you'll need to fill in a bit more of the details...

• Will Mr X be making his annual retirement withdrawals at the END of each year; i.e. will the first retirement withdrawal be at the end of Year 21, or immediately upon retirement (which would be the first day of Year 21)?
• Is the amount he has currently saved $50K or $500K? (You've got an inconsistency in your data.)
• Will his 20 annual contributions be made at the end, or beginning, of each year? In other words, will his first contribution be made today, or one year from today?

In the meantime, break the problem down and attack it along these lines:

• If he wants to draw 100K per year in perpetuity, how much he have accumulated one year prior to his first draw?
• After determing the necessary amount in the previous point, how much of that will be furnished by his present savings, assuming it grows at 10% pa?
• The portion of the targeted ending amount NOT furnished by the growth of the current savings must then be furnished by the annual contributions he'll be making.

For that last one, you can use a "future value of an annuity" formula, to which I'd guess you've probably had some exposure, judging from your question.

Let us know how you've proceeded to this point, and we can be of further help.

Yes Mr. X will be making payments at the end of the year.

also it is $50,000 not $500,000.

Okay, you've answered the 2nd and 3rd of my three questions, so for the first I'll assume that X will be making his annual retirement withdrawals at the end of each year, with the first occurring at the end of Year 21.

Your proposed answer for (a) is incorrect (hint: too high).

Show what your calculations have been, and elaborate a bit on your understanding of the problem, and where you're confused. We'll be glad to help steer you onto the right track.

I've never done one of these "in perpetuity" ones. So how do you decide how much you need at retirement? ArcSine, you can PM me on that if you don't want to give away the homework.

Never mind... I get it. :rolleyes: