Correct spelling, explanation: interest is a noun originated in Latin and it was derived from the verb interesse, consisting of two elements: the prefix inter and the verb esse which denoted to be between. This is the reason why nowadays we spell this word as interest, not intrest.

Definition of interest:
noun/verb, your interest is something that you enjoy doing and spend a lot of time learning about it,
Photography is one of many interests that I have.
The stories about his personal life have lost my interest in the book.

Phrases with interest:
have a keen interest in something – to be very fascinated by something,
Mike hadn’t realized that Dennis had such a keen interest in playing the piano until he listened to him.
take an interest in someone or something – to be or become curious about someone or something,
She promised to take an interest in my cat during my absence from home.

Incorrect spelling, explanation: the word intrest does not exist in English. In Latin, there was the prefix inter, not intr that created the noun interest. A similar form was in Old French and we cannot notice any change in the spelling of this word. However, the learners may make mistake writing intrest due to its pronunciation as /ˈɪntrest/. To sum up, the exclusively correct form is interest, intrest is incorrect.

Incorrect spelling

Incorrect spelling

Incorrect spelling