The story
Receipt came from Anglo-Norman receite, and Middle English wrote it receyt; it is recorded from the 1380s, when it meant the list of ingredients in a medicine. The French word had no P, and neither did the English one.
Its Latin ancestor did: receptus, from recipere, "to receive". As with debt and doubt, writers later inserted the P so the spelling would point to the Latin. The sound never followed.
The word has a famous twin. Recipe is Latin recipe, "take!" — the first word a doctor wrote on a prescription — and for centuries English used receipt to mean a recipe for food or medicine. Old cookbooks are full of "receipts". Eventually recipe took over that job and receipt settled on the written proof that you received something.
