Formulas and sources
Each formula this calculator uses, where it comes from, and what it leaves out. "How it works" shows the same formula with your own numbers.
Monthly loan payment
Simple, Refinance and Comparison modes
- M
- monthly payment, before any extra payment
- P
- loan amount
- r
- monthly rate: the annual rate ÷ 12
- n
- number of monthly payments
A term in years is rounded to the nearest whole month. At a 0% rate the payment is P ÷ n. Refinance works it out for both loans, and Comparison for each offer.
Source: Standard formula; no single publisher. After 36 payments, the schedule gives the same interest paid and balance as the CFPB's example of a $20,000 five-year auto loan at 5% [1].
Payoff with an extra payment
Simple, Refinance and Comparison modes, when an extra payment is entered
- M
- monthly payment, from the formula above
- extra
- extra monthly payment
- r
- monthly rate
This repeats every month until the balance reaches 0. Interest saved is the scheduled interest, M × n - P, less the interest actually paid with the extra payment.
Source: Standard formula; no single publisher.
Refinance breakeven
Refinance mode
- Breakeven (months)
- months until the payments saved reach the refinancing fees
Each loan's payment, extra included, counts until that loan is paid off and as 0 after it. With no fees and a lower new payment, breakeven is immediate. The Mortgage Calculator measures breakeven differently: closing costs and points ÷ the monthly saving.
Source: CalcTrail's own measure; no publisher.
Lifetime savings
Refinance mode
- Lifetime savings
- what refinancing saves over both loans; below 0, what it costs
Each loan's interest comes from its own schedule. A larger or smaller new loan amount, such as cash taken out, is not counted as a saving or a cost.
Source: Arithmetic on the payment formula above; no single publisher.
Payoff strategies
Simple mode, in the Loan Optimization panel
Each strategy runs month by month like the extra payment above, against the plain schedule. Bi-Weekly Payments adds one twelfth of the payment every month, one extra payment a year; a real plan pays half the payment every two weeks, so its interest can differ slightly. 10% Extra Payment adds a tenth of the payment, Round Up Payment takes it to the next multiple of $50, and Double Principal Payment pays that month's principal part again.
Source: Standard formula; no single publisher. The bi-weekly plan's yearly total follows the CFPB's definition [2].
Sources
- Consumer Financial Protection Bureau. Quarterly Consumer Credit Trends: Growth in Longer-Term Auto Loans, page 6. November 2017.
- Consumer Financial Protection Bureau. Mortgages key terms, Bi-weekly payment. Page last modified December 28, 2022.
What this calculator does not cover
- This is a general installment loan calculator. Its only fee is the one-time refinancing cost in Refinance mode; sales tax and origination fees are not modeled. For a home purchase with PMI, property tax and insurance, use the Mortgage Calculator; for a car with a trade-in, negative equity or fees, use the Car Loan Calculator.
- Interest is charged once a month at the annual rate ÷ 12. A lender that charges interest daily, or a variable rate, gives a different schedule.
Sources checked on .