Break-Even Point Calculator for Consolidation Loans
Find out how many months it takes for a consolidation loan to break even — i.e., when total payments on the new loan equal (and then beat) what you would have paid keeping your existing loans.
Formulas Used
Monthly Payment:
M = P × r × (1 + r)ⁿ / ((1 + r)ⁿ − 1)
Where P = principal, r = monthly interest rate (annual rate ÷ 12), n = number of monthly payments.
If the interest rate is 0%: M = P / n
Cumulative Cost at Month t:
Cumulative Cost(t) = M × min(t, n)
Payments stop once the loan is fully paid off.
Break-Even Month:
The first month t where the cumulative cost of the consolidation loan ≤ cumulative cost of the existing loans:
M_new × min(t, n_new) ≤ M_old × min(t, n_old)
Total Savings:
Savings = (M_old × n_old) − (M_new × n_new)
Fees: Origination/closing fees are added to the consolidation loan principal: P_new = Balance + Fees
Assumptions & References
- All existing loans are modeled as a single equivalent loan using the weighted average interest rate and remaining term.
- The consolidation loan uses standard amortization (fixed monthly payments, interest compounded monthly).
- Origination or closing fees are assumed to be rolled into the new loan balance rather than paid upfront.
- No prepayment penalties are assumed on either the existing or consolidation loans.
- The break-even point is defined as the first month at which cumulative payments on the consolidation loan are less than or equal to cumulative payments on the original loans.
- Tax deductibility of interest (e.g., student loan interest deduction) is not considered; consult a tax advisor.
- Formula reference: Standard loan amortization — Consumer Financial Protection Bureau (CFPB), consumerfinance.gov.
- Break-even methodology consistent with guidance from Investopedia: Debt Consolidation.