<prompt> Human: Hi folks!I am on board with the avalanche method being mathematically more efficient than the snowball method.However, I am trying to understand the subtleties of the theory. Basically everyone is saying just pay the loans with the highest interest rates first and basically ignore the principle balances.What happens when I have such a high principal, that the daily accrued interest is actually greater than a loan with a lower principle but higher interest rate?Example: I have 3 loans.Loan 1:Principal 42,722.00; Interest rate 6.8; Daily Accr. Int. 7.95Loan 2:Principal 40,500.00;Interest rate 5.41; Daily accr. int. 6.00Loan 3:Principal 8,155.00; int. rate 7.21; Daily accr. int. 1.61My question is do I throw payments at Loan 1 and 2 since they actually accrue more interest? Or do I attack Loan 3 since it has the highest interest rate, despite having the lowest daily accrued interest?The former seems more logical to me, but I may be missing something here.Also, not sure if this makes a difference, but these are medical student loans. Planning on entering income based repayment plan during residency and all payments will be going towards interest and no principal. My understanding is I basically want to keep interest from growing out of control. So is the underlying objective of the avalanche method to actually minimize accrued interest in this situation?Thanks!Update:Thanks for the awesome answers so far everyone! I am convinced that paying the highest interest rate loan is the way to go when destroying debt.My related follow-up question pertains to paying off as much accrued interest on these loans as much as possible before the interest is capitalized into the principal.Since the loans have different ages they have different amounts of total accrued interest.Same loans as above: Loan 1 has 12,000 Loan 2 has 7000 Loan 3 has 1000My follow question is does the same Avalanche theory apply to this situation? Basically do I pay off that 1000 in accrued interest on Loan 3 before paying the accrued interest on 1 and 2? This is all without paying any principal so I can minimize capitalization  <response>: Or do I attack Loan 3 since it has the highest interest rate, despite having the lowest daily accrued interest?This one.You are getting mixed up because you are looking at absolute numbers right now and with the lower interest rate loans having such higher balances, it is throwing you off.Your Loan 1 has 5.24 times more principal than Loan 3. So if we adjusted the daily interest accrued of Loan 3 to 5.24 times so that it was as if Loan 3 had the same principal as Loan 1, then Loan 3 would have 8.43 in daily accrued interest. You can see that is higher than the 7.95 Loan 1 has. Loan 3 is simply accruing daily interest at a faster rate than Loan 1. That is why you want to attack that loan first. 