According to Title 18, Section 333 of the United States Code, it is illegal to mutilate, deface, disfigure, or destroy currency with the intent to render it unfit for circulation. Burning US dollar bills is unlawful if the objective is to render the money unusable.
So no doing the burn.
$60 -$70 would be worth having backup power at home or at Bug Out site. Better than waiting for Solar power to charge up, All it would have to do is maintain as needed.