This overlaps a lot with "I'll call you when I get there", in terms of challenging the "strength" of "will".
Here are two pieces of culture for a start. Consider the Terminator's very famous "I'll be back":
(Interestingly enough, this particular English construct of "I'll" was hard for Arnold to say)
Listen also to Wayne's way of saying "She will be mine -- oh yes, she will be mine" in Wayne's World:
Indeed, it does sound rather determined to say:
I will buy that radio.
Not just determined, but robotic. It's such a stark declaration of intention; especially without the "I'll" contraction, that most people just don't talk like that unless they're acting or being funny. Most speakers are more indirect: "I'm planning on buying that radio someday" or "I'm looking at different radios, and I think this is the one I'll probably get" would be more comfortable.
But if you said:
I will buy that radio!
That could be completely joking. You could be with a friend at a store and find the ugliest and most outdated radio on the planet. The emphasis on THAT is to call out how ridiculous it is. Then, the "will" fades into the background completely; as you have no serious intent to buy anything whatsoever.
But can this OALD’s meaning for 'will', "used for showing that somebody is willing to do something," include strong determination in the Collins's example: I will buy that radio (even) if it’s the last thing I do? Consulting OLAD's account for 'willing,' "not objecting to doing something; having no reason for not doing something," I'm not quite sure if it can.
I will buy that radio doesn't need the "if it's the last thing I ever do", and actually adding that cliche line makes it sound like the speaker thinks the whole thing is a joke. "if it's the last thing I ever do" has really only been popularized by exaggerated and over-dramatic cartoon characters as from Looney Tunes; no one says it without intending to be funny.
Really you're dealing with a sentence that native speakers would tend to nuance in some way to avoid sounding robotic or weird in terms of the strength of intent you are asking about.