joellewis/debt-management

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 interest on its full $12K balance throughout the earlier phases, not just at the end).
5. Total: 26 months, ~$1,946 total interest.

Solution — Snowball (smallest balance first: $3K → $5K → $12K):

1. Extra $500 goes to personal loan ($575/mo total to PL).
2. Personal loan ($3K at 15%, $575/mo): paid off in month 6, ~$123 interest.
3. Freed payment rolls to the credit card ($100 + $575 = $675/mo): paid off in month 14, ~$911 interest.
4. All payments roll to the student loan: paid off in month 26, ~$1,071 interest.
5. Total: 26 months, ~$2,104 total interest.

Comparison: Avalanche saves ~$158 in interest; both finish in 26 months. The difference is modest because the highest-rate debt is not the largest. Snowball gives a quicker first win (month 6 vs month 10 to first payoff) — for many people that motivational difference is worth $158.

Example 2: Refinance breakeven

Given: Current mortgage: $300K remaining, 6.5%, 25 years left, payment $2,028/mo. New offer: 5.5%, 25 years, closing costs $6,000, payment $1,838/mo. Calculate: Breakeven period and total interest savings. Solution:

1. Monthly savings: $2,028 - $1,838 = $190/month.
2. Breakeven: $6,000 / $190 = 31.6 months ≈ 32 months (2 years 8 months).
3. If staying in the home beyond 32 months, refinancing saves money.
4. Total payments (old): 25 × 12 × $2,028 = $608,400 → total interest = $608,400 - $300,000 = $308,400.
5. Total payments (new): 25 × 12 × $1,838 + $6,000 = $557,400 → total interest = $557,400 - $300,000 = $257,400.
6. Total interest savings: $308,400 - $257,400 = $51,000.

Common Pitfalls

• Ignoring psychological factors — snowball works better for many people despite costing slightly more in interest
• Not including all closing costs in refinancing analysis (origination fees, appraisal, title insurance, points)
• Consolidation at a lower rate but longer term may cost more in total interest — always compare total cost
• Paying off low-rate debt instead of investing (opportunity cost) without considering risk tolerance and guaranteed vs uncertain returns
• Not considering tax deductibility of mortgage or student loan interest when comparing effective rates
• Making only minimum payments on high-interest debt while saving in low-yield accounts
• Consolidation freeing up credit lines that lead to new debt accumulation
• Ignoring the amortization reset: refinancing to a new 30-year term extends the payoff date

Cross-References

• lending: mortgage analysis, loan terms, and amortization calculations
• emergency-fund: adequate emergency fund prevents taking on new high-interest debt during crises
• savings-goals: debt payoff competes with savings goals for cash flow allocation
• tax-efficiency: tax deductibility of certain debt interest affects optimal payoff order
• liquidity-management: debt payments are fixed obligations in cash flow planning
• financial-planning-workflow (advisory-practice plugin): debt payoff strategies are evaluated during the cash flow and recommendation phases of financial planning

Running the Script

uv run scripts/debt_management.py            # run the demo (uses PEP 723 inline deps)
uv run scripts/debt_management.py --verify   # check demo outputs against the worked examples (exit 1 on mismatch)
python3 scripts/debt_management.py            # alternative (requires: pip install numpy)

The demo prints the calculations covered above; its values match the worked examples in this skill. Run --help for a list of the classes and functions. For programmatic use, import the module rather than running it — the demo only executes under python debt_management.py.