Why does the debt avalanche method lead to greater long-term savings, despite potentially being psychologically harder to implement than the debt snowball method?

The debt avalanche method prioritizes paying off debts with the highest interest rates first, regardless of the outstanding balance. This strategy results in greater long-term savings because it minimizes the total interest paid over the entire debt repayment period. By focusing on the debts that accrue the most interest, the avalanche method effectively reduces the overall cost of borrowing. In contrast, the debt snowball method focuses on paying off the smallest debts first, providing quick psychological wins, but it doesn't necessarily target the highest interest rates. While the snowball method can be motivating, it often leads to paying more interest overall because higher-interest debts accumulate interest for a longer period. The avalanche method's focus on minimizing interest charges mathematically guarantees the lowest total cost, assuming consistent application and resources allocated to debt repayment. The long-term savings are directly proportional to the difference in interest rates between the debts and the total amount of debt outstanding; the greater the difference and the higher the debt, the more substantial the savings will be with the avalanche method.