CalcDomain

Authoritative Data Source & Methodology

Primary Sources:

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

Amortized payment (per period):

\[ PMT = P \cdot \frac{i}{1-(1+i)^{-n}} \]

where \(P\) = principal, \(i\) = periodic rate \(= \frac{APR}{m}\), \(n\) = total number of payments, \(m\) = payments per year.

Total interest: \[ I_{\text{total}} = PMT \cdot n - P \]
Total cost: \[ C_{\text{total}} = P + I_{\text{total}} + \text{fees} \]

Extra payments reduce balance each period and shorten the payoff time; the algorithm iteratively applies extra principal and recomputes interest on the remaining balance.

Glossary of Variables

  • Amount (P): Initial loan principal.
  • APR: Annual percentage rate, converted to periodic rate \(i=APR/m\).
  • Term: Loan length in years or months, converted to total payments \(n\).
  • Fees: One-time upfront costs (origination, points, closing costs).
  • Payment/period: Scheduled payment amount at the chosen frequency.
  • Total interest: Sum of interest over the life of the loan.
  • Total cost: Principal + total interest + fees.
  • Breakeven: Time where cumulative cost of one loan becomes lower than another.

How It Works: A Step-by-Step Example

Scenario: Compare Loan A (APR 6.25%, fees $2,500) vs Loan B (APR 6.00%, fees $5,000), both $250,000 for 30 years, monthly payments, with no extra payments.

  1. Compute \(m=12\), \(i_A=0.0625/12\), \(i_B=0.06/12\), \(n=360\).
  2. Calculate each payment using \(PMT\). Lower APR generally yields a lower payment.
  3. Total interest is \(PMT\cdot n - P\); add fees to get total cost.
  4. Breakeven considers the higher upfront fees versus the monthly savings from the lower APR.

Frequently Asked Questions

Why use APR instead of nominal rate?

APR standardizes costs across lenders by reflecting certain fees in an annualized rate, improving apples-to-apples comparisons.

Are fees financed or paid upfront?

This tool treats “One-time Fees” as paid upfront for total cost comparison. If fees are financed, you can add them to the loan amount.

How accurate is the breakeven estimate?

It’s a practical estimate using cumulative cost curves given your inputs. Official disclosures may differ slightly due to compounding conventions and fee treatment.

Does biweekly really pay off faster?

Biweekly has 26 payments per year, slightly more than monthly 12×. This typically leads to faster payoff and lower interest, all else equal.

Can I export or print the schedule?

Yes. Use the Print button for a clean, printer-friendly schedule of the lowest-cost loan.

Tool developed by Ugo Candido. Content verified by CalcDomain Editorial Board.
Last accuracy review: