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Advanced Math/Annuity Computation


Each year of sick leave increases your retirement annuity by one percent, each month by .0833 percent. Because annuities are based on years and full month of service, the exact amount of credit you'll get for your unused sick leave depends on whether you have any days of actual service that don't equal a full month. Any leftover days of actual service will be converted into retirement hours and added to those unused sick leave hours. For retirement purposes, all days are 5,797+ hours long. (Divide 2,087 by 360 which is 12 30-day months) - As a result, an annuity month is approximately 174 hours long. When the extra months are counted up, any days that didn't add up to a full month are discarded.

32 years - 3 months of service 468 hours of sick leave $32,000 a year annuity

How much will the 468 hours of sick leave add to the annuity each year?

I had a hard time understanding the question—it wasn't stated very clearly. However, here is my take on it:

468 hours × 1 annuity month/(174 hours) ≅ 2.69 months, which is rounded down to 2 months.
The proportional increase resulting from the 2 months is 1.000833².
32,000 dollars/year × 1.000833² ≅ 32,053.33 dollars/year
$32,053.33 - $32,000 = $53.33

The 468 hours of sick leave increases the annuity by $53.33 per year.

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