<prompt> Human: I have some students loans to pay off, and it looks like the best strategy is to pay off the highest-interest loans first. I searched around a bit, and the only reasoning Ive seen goes something like heres an example of avalanche vs. snowball payment, avalanche wins. However, I have not seen an actual proof. Could someone direct me to one? More math the better. Ill have a go at this, but Im sure somebody has already shown this to be true.  <response>: You dont have to get fancy, because a dollar is a dollar. So, if you have one pile of dollars accruing interest at 12, that means that each dollar accrues 0.12 in interest in year. If you have another pile of dollars accruing interest at 6, each dollar accrues 0.06 in interest each year. How do you save more money, by removing one of the dollars in the 12 pile or the 6 pile? Theres no math to get around the simple fact that more interest accrues on the 12 loan, so there is always more benefit to paying off one of those 12 dollars. 