Final answer:
Bill Gates was 13 years old when he created his first computer program in collaboration with Paul Allen.
Step-by-step explanation:
The main answer to the question of at what age Bill Gates invented his first computer program with Paul Allen is option B) 13. Bill Gates showed early interest and aptitude in computer programming, and by the age of 13, he had indeed created his first computer program. Collaborating with Paul Allen, Gates developed a version of the programming language BASIC for the first microcomputer - the MITS Altair.