/debt-management

name: debt-management
description: "Provide frameworks for managing and paying off personal debt effectively. Use when the user asks about debt payoff strategies (avalanche vs snowball), refinancing decisions, debt consolidation, debt-to-income ratios, or the opportunity cost of paying off debt vs investing. Also trigger when users mention 'which debt to pay first', 'should I refinance', 'credit card debt', 'student loan payoff', 'DTI for mortgage', 'balance transfer', 'good debt vs bad debt', or ask how to get out of debt faster."

Debt Management

Core Concepts

Debt Avalanche

Pay minimum payments on all debts, then direct all extra payment to the debt with the **highest interest rate** first:

• **Mathematically optimal:** Minimizes total interest paid over the life of all debts
• Once the highest-rate debt is paid off, the freed-up payment rolls to the next highest rate
• Requires discipline — the highest-rate debt may also be the largest balance, meaning slow visible progress initially
• Always saves money compared to snowball, though the difference varies by debt profile

Debt Snowball

Pay minimum payments on all debts, then direct all extra payment to the debt with the **smallest balance** first:

• **Psychologically effective:** Quick wins build momentum and motivation
• Research (Kellogg School) shows people are more likely to stick with snowball and actually become debt-free
• May cost more in total interest than avalanche, but adherence is higher
• Best for individuals who need motivational wins to stay committed

Debt-to-Income Ratio (DTI)

Total monthly debt payments expressed as a percentage of gross monthly income:

• **Front-end DTI (housing ratio):** Monthly housing costs (PITI: principal, interest, taxes, insurance) / gross monthly income
• Guideline: < 28%
• **Back-end DTI (total debt ratio):** All monthly debt payments (housing + car + student loans + credit cards + other) / gross monthly income
• Guideline: < 36% (conventional), up to 43% (FHA), some lenders allow up to 50% for qualified borrowers
• DTI is a key factor in mortgage qualification and overall financial health assessment

Refinancing Analysis

Compare the total cost of the existing loan vs the new loan, accounting for closing costs:

• **Monthly savings:** Old payment - new payment
• **Breakeven months:** Total closing costs / monthly savings
• **Total cost comparison:** Sum of all remaining payments (old) vs sum of all payments (new) + closing costs
• If you plan to keep the loan beyond the breakeven point, refinancing saves money
• Consider: remaining term, resetting the amortization clock, and cash-out implications

Debt Consolidation

Combine multiple debts into a single loan, ideally at a lower interest rate:

• **Potential benefits:** Lower rate, single payment, simplified management
• **Risks:** Longer term may increase total interest even at lower rate; freed-up credit lines may tempt new borrowing
• **Evaluate:** Compare total interest paid (all debts independently) vs total interest paid (consolidated loan)
• Balance transfer cards (0% intro rate) can be effective but require payoff before the rate expires

Good Debt vs Bad Debt

• **Good debt:** Low interest rate, potentially tax-deductible, finances an appreciating asset or increases earning power (mortgage, student loans, business loans)
• **Bad debt:** High interest rate, finances depreciating assets or consumption (credit cards, payday loans, auto loans on luxury vehicles)
• The line is not absolute — a low-rate auto loan for a reliable commuter car can be reasonable

Opportunity Cost Analysis

When debt carries a low interest rate, paying it off aggressively may not be optimal:

• **Decision rule:** If expected after-tax investment return > after-tax debt interest rate, investing the extra cash may build more wealth
• **Example:** 3.5% mortgage (2.5% after tax deduction) vs 7-10% expected equity returns — investing likely wins mathematically
• **Caveats:** Investment returns are uncertain, debt payoff is guaranteed; psychological benefit of being debt-free has real value
• Consider risk tolerance: guaranteed 3.5% return (debt payoff) vs variable 7-10% (investing)

Debt Payoff Timeline

Amortization calculation with extra payments:

• Standard amortization: n = -ln(1 - (P×r)/PMT) / ln(1+r)
• With extra payment: replace PMT with PMT + extra, recalculate n
• Total interest = (n × PMT) - P (adjusting for extra payments)

Key Formulas

| Formula | Expression | Use Case | |---------|-----------|----------| | Front-end DTI | Housing payments / gross monthly income | Mortgage qualification | | Back-end DTI | All debt payments / gross monthly income | Overall debt health | | Refinance breakeven | Closing costs / monthly savings | Months to recoup refi costs | | Months to payoff | n = -ln(1 - Pr/PMT) / ln(1+r) | Debt payoff timeline | | Total interest paid | (n × PMT) - Principal | Cost of borrowing | | Effective rate (after tax) | r × (1 - marginal_tax_rate) | Tax-deductible debt comparison |

Worked Examples

Example 1: Avalanche vs snowball comparison

**Given:** Three debts with $500/month available for extra payments (above minimums):

• Credit card: $5,000 balance, 22% APR, $100 minimum
• Student loan: $12,000 balance, 6% APR, $200 minimum
• Personal loan: $3,000 balance, 15% APR, $75 minimum

**Calculate:** Order of payoff, total months, and total interest for each strategy (month-by-month simulation; see `scripts/debt_management.py`). **Solution — Avalanche (highest rate first: 22% → 15% → 6%):** 1. Pay minimums on all ($375/mo). Extra $500 goes to credit card ($600/mo total to CC). 2. Credit card ($5K at 22%, $600/mo): paid off in month 10, ~$476 interest. 3. Freed payment rolls to the personal loan ($75 + $600 = $675/mo to PL): paid off in month 14, ~$408 interest. 4. All payments roll to the student loan ($200 + $675 = $875/mo): paid off in month 26, ~$1,062 interest (the 6% loan accrues