Math CentralQuandaries & Queries


Question from Kenneth:


I have a question regarding how the units cancel in the following:

A company uses the following calculation to determine the monthly payment for its employees as they retire:

1.1% * average 5 years highest salary * years of service

If an employee worked 33 years and his average 5 year salary is $\$30,705.17,$ what is his monthly payment?

I used the following to determine his monthly payment, but I am not sure how the units cancel especially the years.

1.1% * $\$30,705.17$ * 33 years divided by 12 months/year

I determined his payment as $\$928.83$ per month, but the year units do not cancel unless the 1.1% is per year.

Is the correct calculation 1.1%/year * $\$30,705.17$ * 33 years divided by 12 months/year so that the units cancel properly?

The $\$30,705.17$ is an average for 5 years of working. It is not $\$30,705.17$ per year.

I thank you for your assistance.

Hi Kenneth,

The expression

\[1.1\% \times \mbox{ average 5 years highest salary } \times \mbox{ years of service}\]

determines the annual payment. To obtain the monthly payment you need to divide by 12 which you did. With an average 5 years highest salary of $\$30,705.17$ and 33 years of service I got a monthly payment of $\$928.83$ as you did. But what about the units?

The figure 30,705.17 is in the units of dollars per year so the calculation for the annual pension payment is

\[1.1\% \times 30.705.17 \frac{\mbox{dollars}}{\mbox{year}} \times 33 \mbox{ years } = \$11,145.98\]

which, divided by 12, is $\$928.83$ per month.


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