

Subject:
Finding Jill Moran's Retirement Annuity
Category: Business and Money > Finance Asked by: chickaga List Price: $5.00 
Posted:
22 Nov 2003 16:18 PST
Expires: 22 Dec 2003 16:18 PST Question ID: 279481 
Sunrise Industries wishes to accumulate funds to provide a retirement annuity for its vice president of research, Jill Moran. Ms. Moran by contract will retire at the end of exactly 12 years. Upon retirement, she is entitled to receive an annual endofyear payment of $42,000 for exactly 20 years. If she dies prior to the end of the 20year period, the annual payments will pass to her heirs. During the 12year "accumulation period" Sunrise wishes to fund the annuity by making equal annual endofyear deposits into an account earning 9% interest. Once the 20year "distribution period" begins, Sunrise plancs to move the accumulated monies into an account earning a guaranteed 12% per year. At the end of the distribution period, the account balance will equal zero. Note that the first deposit will be made at the end of year 1 and that the first distribution payment will be received at the end of year 13. answer B. How large a sum must Sunrise accumulate by the end of year 12 to provide the 20year, $42,000. annuity? 

Subject:
Re: Finding Jill Moran's Retirement Annuity
Answered By: omnivorousga on 23 Nov 2003 05:01 PST Rated: 
Chicka  This calculation requires 20 separate calculations to arrive at the endofyear 12 number. Let's start with what we know, then work backwards. * At the end of year 20, the last principal payment will zero the account * Interest will also be paid at 12% * Total payment = $42,000 YEAR 20: So, we don't know the principal, but let's call it x: .12*x + x = $42,000 solve for x: 1.12x = $37,500 YEAR 19: Now we'll see the interest benefit of 12% on that $37,500 in principal, plus another chunk of principal paid from the annuity. That additional chunk of principal is y: .12 ($37,500 + y) + y = $42,000 $4,500 + .12y + y = $42,000 1.12y = $37,500 y = $33,482 YEAR 18: Total principal on which interest is paid is now $37,500 + $33,482 + the piece of principal paid this year (z), so we run the calculation again: .12 ($70,982 + z) + z = $42,000 $8518 + 1.12z = $42,000 1.12z = $29,895 We could keep going or perform the same calculation in a spreadsheet 17 more times: .12 * (endofyear principal + this year's principal) + this year's principal = $42,000 The spreadsheet calculation is made easier by the fact that .12*(endofyear principal) is the next year's interest. So, year 17 will have interest of .12 ($37,500 + $33,482 + $29,895) = $12,105; principal paid during the year is now calculated as: ($42,000$12,105)/1.12 = $26,692 The iterations are shown in the spreadsheet here, which is viewable in your browser, even if you don't have Excel: http://www.mooneyevents.com/annuity.xls Thus, the endofyear 12 number  the one that STARTS the retirement annuity  is $313,716.74, which will provide Jill Moran with $37,646 in interest and $4,354 at the end of her first year of retirement. We haven't done the hard part of this annuity calculation  finding the amount that needs be paid in each year. Here is how that is done (and thank goodness for spreadsheets): http://answers.google.com/answers/threadview?id=122589 If any aspect of this answer is not clear, please post a clarification request before rating this Google Answer. Best regards, OmnivorousGA  
 
 
 

chickaga
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Problem answered thank you. Clarification is needed in order to interpret equation answer to problem. chicka 

Subject:
Re: Finding Jill Moran's Retirement Annuity
From: probonopublicoga on 23 Nov 2003 05:37 PST 
Hmmmmm But where would you find 12% pa guaranteed over 20 years? Or even 9% pa over 12 years? 
Subject:
Re: Finding Jill Moran's Retirement Annuity
From: omnivorousga on 23 Nov 2003 09:25 PST 
Probono  You remember 1980  you could get 15% returns! Of course, inflation was 12%. . . 
Subject:
Re: Finding Jill Moran's Retirement Annuity
From: probonopublicoga on 23 Nov 2003 13:53 PST 
Yeah .... but 12% guaranteed over 20 years? Never in my lifetime ... And I've just turned 100. 
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