Data Source and Methodology
The calculator uses the standard amortization identity referenced by the Consumer Financial Protection Bureau (CFPB) and Truth in Lending (Regulation Z) Appendix J. Each debt is amortized separately using your specified payment; the consolidation loan uses the APR and term you enter. Origination fees can be financed (added to the new loan amount) or paid upfront.
Formulas Used
Monthly rate: \( r = \dfrac{\text{APR}}{12 \times 100} \)
Months to pay a debt: \( n = \dfrac{-\ln\left(1 - \dfrac{rB}{P}\right)}{\ln(1+r)} \) if \( r > 0 \); otherwise \( n = \dfrac{B}{P} \)
Interest paid on a debt: \( I = n \cdot P - B \)
Consolidation payment: \( P_c = \dfrac{L r_c}{1 - (1 + r_c)^{-N}} \) (or \( L/N \) if \( r_c = 0 \))
Tips before consolidating
- Verify that the new APR and term truly lower total interest, not just monthly payments.
- Look out for origination fees or prepayment penalties on existing debts.
- Consider continuing to pay extra principal even if the new payment is lower to accelerate payoff.
Formula (LaTeX) + variables + units
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Monthly rate: \( r = \dfrac{\text{APR}}{12 \times 100} \) Months to pay a debt: \( n = \dfrac{-\ln\left(1 - \dfrac{rB}{P}\right)}{\ln(1+r)} \) if \( r > 0 \); otherwise \( n = \dfrac{B}{P} \) Interest paid on a debt: \( I = n \cdot P - B \) Consolidation payment: \( P_c = \dfrac{L r_c}{1 - (1 + r_c)^{-N}} \) (or \( L/N \) if \( r_c = 0 \))
- P = principal (loan amount) (currency)
- r = periodic interest rate (annual rate ÷ payments per year) (1)
- n = total number of payments (years × payments per year) (count)
- M = periodic payment for principal + interest (currency)
- E = extra principal payment per period (currency)
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Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.