The Mathematics of Revolving Credit: Negative Amortization Traps, Minimum Payment Recurrences, and Debt Avalanche Algorithms
Credit cards are among the most asymmetric debt instruments in modern financial systems. With APRs routinely exceeding 20% to 30%, compounding balances create rapid interest accrual that overwhelms standard minimum payments. Below is an exhaustive quantitative dissection of revolving credit mathematics, daily periodic rate calculations, and algorithmic debt elimination models.
1. Daily Balance Compounding & Finance Charges
Unlike installment loans (mortgages, auto loans) where interest compounds monthly, credit cards compute interest using the Average Daily Balance (ADB) method compounded on a 365-day basis.
ADB = Sum of daily ledger balances divided by total days in billing cycle.
APR = Stated annual percentage rate (e.g. 0.2199 for 21.99%).
Billing Days = Typically 28 to 31 days per billing period.
2. Debt Avalanche vs. Debt Snowball: Mathematical Optimality
When managing multiple credit cards, two primary algorithmic repayment frameworks exist:
Debt Avalanche (Mathematically Optimal)
Allocates all surplus capital to the card with the highest APR first, minimizing total interest paid and reducing debt payoff duration to its theoretical minimum.
Debt Snowball (Behavioral Momentum)
Targets the card with the lowest absolute balance first, generating rapid psychological victories by eliminating individual accounts regardless of APR differentials.