Overall Payment Reduction Strategy:
This strategy allocates extra funds fractionally across all loans. It first targets accrued interest to prevent capitalization and then applies any remaining funds to the principal. By reducing the principal, it decreases future interest accrual. This method follows a greedy approach—similar to the fractional knapsack problem—by prioritizing loans with higher interest rates.
Monthly Payment Reduction Strategy (0/1 Knapsack):
This strategy focuses on lowering monthly payment obligations by fully paying off certain loans. It treats each loan as an “item” that yields a benefit only if it is completely paid off. The algorithm searches for the best combination of loans that can be fully eliminated with the available extra payment, using a brute-force approach.
Fractional Monthly Payment Reduction Strategy:
This new approach allows fractional allocation toward reducing monthly payments. For each loan, the full payoff amount (principal plus accrued interest) and the full monthly payment (if the loan were completely paid off) are computed. Extra funds are then allocated based on the marginal benefit (monthly payment saved per dollar needed). Even if a loan isn’t fully paid off, making progress toward the payoff threshold provides a proportional benefit.
These strategies offer complementary insights: while the overall strategy reduces total debt and future interest accrual, the monthly payment strategies focus on lowering your monthly obligations—either by completely eliminating loans or by capturing incremental benefits.