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Q: Finding Jill Moran's Retirement Annuity ( Answered ,   3 Comments )
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 Subject: Finding Jill Moran's Retirement Annuity Category: Business and Money > Finance Asked by: chicka-ga 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 end-of-year payment of \$42,000 for exactly 20 years. If she dies prior to the end of the 20-year period, the annual payments will pass to her heirs. During the 12-year "accumulation period" Sunrise wishes to fund the annuity by making equal annual end-of-year deposits into an account earning 9% interest. Once the 20-year "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 20-year, \$42,000. annuity?```
 Subject: Re: Finding Jill Moran's Retirement Annuity Answered By: omnivorous-ga on 23 Nov 2003 05:01 PST Rated:
 ```Chicka -- This calculation requires 20 separate calculations to arrive at the end-of-year 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 * (end-of-year principal + this year's principal) + this year's principal = \$42,000 The spreadsheet calculation is made easier by the fact that .12*(end-of-year 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 end-of-year 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, Omnivorous-GA``` Request for Answer Clarification by chicka-ga on 23 Nov 2003 07:14 PST ```Hello, Yes, .12*x + x = \$42,000 solve for x 1.12x = 37,500 are you saying that... .12*1.12 + x = 42,000 what is the visual equation to derive at 37,000?``` Clarification of Answer by omnivorous-ga on 23 Nov 2003 09:24 PST ```> .12*1.12 + x = 42,000 > what is the visual equation to derive at 37,000? The above (marked with >) is incorrect. For Year 20, it's the first line that you'd typed: .12*x + x = \$42,000 The first term is the interest; the second term the principal returned to Jill. Best regards, Omnivorous-GA``` Request for Answer Clarification by chicka1-ga on 02 Dec 2003 08:14 PST ```Hello, where did you get 1.12x from to equal 37,500? thank you. chicka-ga``` Clarification of Answer by omnivorous-ga on 02 Dec 2003 09:34 PST ```Chicka -- In proper math terms it should be 1.12x = \$42,500, as that's one year's interest; x = \$37,500 That's how you start working backwards on the interest + principal sides. My apologies for the shorthand . . . Best regards, Omnivorous-GA```
 chicka-ga rated this answer: and gave an additional tip of: \$5.00 ```Problem answered thank you. Clarification is needed in order to interpret equation answer to problem. chicka```

 ```Hmmmmm But where would you find 12% pa guaranteed over 20 years? Or even 9% pa over 12 years?```
 ```Probono -- You remember 1980 -- you could get 15% returns! Of course, inflation was 12%. . .```
 ```Yeah .... but 12% guaranteed over 20 years? Never in my lifetime ... And I've just turned 100.```