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If Mrs. AlphaMicra keeps an eye on the finances at all, a mysteriously missing $500 is a recipe for disaster. If Alpha can convince his parents to buy it for the him to use so the grandchild can use...

I'd see if you can store it on your parent's farm. Then it won't be cluttering up your own home, which takes away one of the arguments. Explain to her you'll only be getting parts from the junk...

At $500, better to ask forgiveness then permission :) Do you have or plan to have kids? Say you're thinking of it a first car for them.