Explanation:

BASIC (Beginner's All-purpose Symbolic Instruction Code) was developed in $1964$ at Dartmouth College with the explicit goal of providing a simple, easy-to-learn programming language for students and beginners, particularly those outside of science and mathematics fields. Its straightforward syntax and interactive environment made it highly accessible for learning fundamental programming concepts. (a) commercial purpose: Incorrect. COBOL is designed for commercial purposes. (b) scientific calculation: Incorrect. Fortran is designed for scientific calculations. (c) to teach a child: While it can be used for this, (d) is a more comprehensive and accurate description of its original design intent. (d) simple language for beginners: Correct. This aligns perfectly with the acronym and historical purpose of BASIC. (e) none of these: Incorrect, as (d) is the most accurate description.