 A Useful Approximation

I saw a video post from the Whitehouse that asked a simple question: "If someone works full time and makes the federal minimum wage, do you know how much their annual salary is?" In the video, an interviewer went around asking people that question, and most of the responses shown were way off the mark.  It is clear that the people featured in the video never learned a simple method to approximate an annual salary from an hourly wage.

Approximating an Annual Salary from an Hourly Wage (assuming a 40 hr workweek):

To approximate an annual salary from an hourly wage, simply double the hourly wage, and move the decimal point three places to the right (multiply by 1,000).  For example, if you earn the Federal Minimum Wage of \$7.25 per hour, here is how the approximation works.

Step 1: double the hourly wage, \$7.25 X 2 = \$14.50

Step 2: move the decimal point three places to the right, \$14,500.00

This is only an approximation, but it is a very good one, assuming the person works full-time. The reason it is such a good approximation is that it only leaves off two weeks of pay. The annual salary for a full-time worker making \$7.25 hourly is given by:

Gross Weekly Pay = \$7.25/hr X 40 hrs/week = \$290/week.

Gross Yearly Pay = \$290/week X 52 weeks = \$15,080.00.

If you make this calculation general, we have: hourly wage X 40 hours per week X 52 weeks per year. This expression is equivalent to this one: hourly wage X 40 X 52 = hourly wage X 2080. The 2080 in that expression is a little awkward to work with when performing mental math.

But, if we shorten the year by two weeks, we would have: hourly wage X 40 X 50 = hourly wage X 2000.

By dropping those two weeks, the calculation becomes very easy to use, and for workers who take a two-week, unpaid vacation, the calculation produces their exact gross annual pay.

Here are some more examples:

 Hourly Wage Approximate Yearly Pay Actual Annual Pay \$10.50 \$21,000 \$21,840 \$15.00 \$30,000 \$31,200 \$25.00 \$50,000 \$52,000 \$34.00 \$68,000 \$70,720

A related approximation can be used for half-time work. If a person works just 20 hours per week, the approximation formula is given by: hourly wage X 1000. In other words, just move the decimal place in the hourly wage three places to the right. For example, if your hourly wage is \$8.75 and you work part-time, your approximate yearly earnings will be \$8,750. You can make this even simpler by rounding the hourly wage to a whole number and just multiplying by 1,000.

If you are offered a part-time job making \$12.75 an hour, you can round \$12.75 to \$13 and multiply by 1,000. Hence, you will earn approximately \$13,000 at that job over the course of one year. The actual earnings would be \$13,260, so you can see how decent the approximation is.

Now, if a videographer approaches you on the street to ask, "If someone works full time and makes the federal minimum wage, do you know how much their annual salary is?," you should be able to provide a respectable response.