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Having difficulties working out the 9% and 12% at different period and the time line in this case

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Sunrise Industries wishes to accumulate funds to provide a retirement annuity for its vice president of research,Jill Morgan. Ms. Morgan by contract will retire at the end of exactly 12years. 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 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 plans to move the accumulated monies into an account earning a guaranteed 12% per year. At the end of the ditribution 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.

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The key lies in understanding the problem. Let us break the problem up in 2 parts, part 1 deals with pre- retirement and part 2 deals with post retirement. Please also see the attached Excel Spreadsheet.
<br>
<br>Part 1)
<br>At the end of year 1 the company pays to Jill's retirement fund $x.
<br>At the end of the second year the company pays Jill $x and also the first year amount has accumulated 9% interest. Hence at the second year the amount becomes: $(x+1.09x).
<br>At the end of third year the amount becomes $x +1.09 times ...

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