'Monthly' and 'annual' as descriptors
When I am describing a service that is billed for once a month I write, "This is a monthly service." When describing a service that is billed for once a year I use, "This is an annual service."
Why would using "This is an annually service." sound incorrect? It's as if 'monthly service' is used as shorthand for 'monthly billed service', and 'annual service' is used as shorthand for 'annually billed service'. Is my problem that 'monthly' is used incorrectly in the first case?
Solution 1:
An annually service sounds wrong because it is wrong; you're using an adverb where you need an adjective (annual).
The trick is that the adjective form of "once a month", monthly, just happens to be the same as the adverbial form, monthly; the reader automatically assigns the word to its correct role based on its placement in the sentence.
Solution 2:
No, monthly is used correctly in the first case. You are comparing apples to oranges here (or adjectives to adverbs).
Per The American Heritage Dictionary, 4th edition, annual is defined as:
adj. 1. Recurring, done, or pefomed every year; yearly: an annual medical examination
So annual is an adjective describing an interval. The word annually, on the other hand, is an adverb. Therefore, it cannot be used as you tried to in your sentence: This is an annually service. You could, as you suggest, write: This is an annually billed service. In that instance, the adverb annually is modifying billed, not service.
Month on the other hand is a noun, with the adjective form being monthly. Per The American Heritage Dictionary, 4th edition, monthly is defined as:
adj. 1. Occurring, appearing, or coming due every month: a monthly meeting; monthly rent payments.
It is grammatically correct to use monthly as you suggested: This is a monthly service. (As others have mentioned, monthly is also an adverb meaning once a month; every month. But in this example, it is an adjective.)
Solution 3:
Because the adjective forms of year and month, are annual and monthly respectively, which is what you are using with the noun service.
The adverb forms are annually and monthly, which are used with the verb billed.
The fact that with month, the same form is found for the adjective and the adverb is what was throwing you off.