There is some arbitrariness in what you are going to call (formal) future tense in an almost analytical language. The idea of grammatical categories, including which tenses to look for in a verb, came into English through Latin whose morphology of verbs was considerably richer.
There is also some arbitrariness on the semantic side. There's a continuum from a one off event currently happening, through an event currently planned or desired or expected, toward a more hypothetical future events which is less grounded in present state of things from the speaker's perspective.
The traditional explanation answers your question quite elegantly: You would use the present tense to talk about future events that have some present reality. Notice especially how this resource presents the intermediate "to be going to" form.
One of the comments on the question mentions that English does not have a future tense. That's somewhat true morphologically. "I will" could be interpreted as a present tense of some kind, on par with "I want" or "I am [going to]". Of course, if we accept that even ancient Greek and Latin have had some analytical verb forms, then "I will" is as good a future tense as one can get in American English.
Maybe more surprisingly, the English subjunctive mood comes with formal past and present tenses (and no counterpart of the indicative mood's future tense), although its present tense semantically refers to hypothetical events which are often imagined to happen, or to be learned of, in the future (if at all).
Going back to the indicative mood: it helps to notice that unadorned present tense is very often used in English in the frequentative meaning, i.e., it can be quite unspecific about whether it refers to repeated events in the past, at present, or in the future. The same could be said about some uses of the (formal) future tense, though: "Accidents will happen.".