The raise is just an increment in your annual salary. Let us say you get a raise of 1200$ to your current salary of 3600$ on July 1. This means you get 400$/month for the next 6 months. You do not get (1800 1200)/6 = 500$/month.

My interpretation of "Semiannual raise of $50" is that twice each year, a raise of $50 is done. This raise, however, applies to your annual base salary. That means your ANNUAL salary goes up in the following pattern every 6 months: 1800, 1850, 1900, 1950, and so on. Each time your annual salary goes up, you get, let us say, monthly paychecks of new annual salary divided by 12. Hence the math I showed.

The solution seems to interpret the problem Description as increments that not only raise your annual salary by that increment but also pay you that increment in every 6 month period.

Comments?

Thanks!

>The raise is just an increment in your annual salary. Let us
>say you get a raise of 1200$ to your current salary of 3600$
>on July 1. This means you get 400$/month for the next 6
>months. You do not get (1800 1200)/6 = 500$/month.

No, that's the point: a semiannual raise, by definition, is a raise on your semiannual salary, not a raise on your annual salary.

>My interpretation of "Semiannual raise of $50" is that twice
>each year, a raise of $50 is done. This raise, however,
>applies to your annual base salary. That means your ANNUAL
>salary goes up in the following pattern every 6 months:
>1800, 1850, 1900, 1950, and so on. Each time your annual
>salary goes up, you get, let us say, monthly paychecks of
>new annual salary divided by 12. Hence the math I showed.

That's not how it works in the real world; or, if it does, your boss is dishonest. If I've understood you correctly, you've worked out the salary in the following way:

Salary in the first year = (1800+1850)/2 = 1825
Monthly paycheck: 1825/12 = 152.08 (plus one-third of a cent).

That's not a semiannual raise of $50; that is an annual salary of $1825.

A semiannual raise works like this:

Salary in the first six-month period = 1800/2 = 900 = $150/month
Salary in the second six-month period = 900 + 50 = 950 = $158.33/month
Total salary = 900+950 = 1850 = $154.17/month on average (actually $154.16 and two-thirds, but near enough).

That's more than $2 per month more than you say, a discrepancy of $25 over the whole year.

It may be that the employee receives an annual paycheck, but that makes no difference; it is calculated this way: six months at $150/month plus six months at $154.17/month. If it is calculated any other way, it is not a semiannual raise.

To understand why, imagine the employee leaves his job after one month. How much pay should he receive? According to your definition of a "semiannual raise", he must be paid $152.08. But when he signed the contract, he agreed to a starting salary of $1800 per annum for the first six months, and $152.02 is equivalent to a salary of $1825. He should, in fact, be paid only $150.

>The solution seems to interpret the problem Description as
>increments that not only raise your annual salary by that
>increment but also pay you that increment in every 6 month
>period.

Exactly, because that is what "semiannual raise" means; and it makes no difference whether you are a linguist or a mathematician, it means the same to both.