Authoritative Data Source and Methodology
Primary reference: Truth in Lending (Regulation Z), 12 CFR Part 1026, Appendix J — Annual Percentage Rate computations for closed-end credit. Effective edition (as of 2024). Direct source: eCFR — 12 CFR §1026, Appendix J . All calculations are strictly based on the formulas and data provided by this source.
The Formula Explained
Periodic rate (monthly): \( r = \dfrac{\text{APR}}{12} \)
Number of months: \( n \)
Level-payment amortization:
\( M = \dfrac{P \cdot r}{1 - (1 + r)^{-n}} \quad \text{for } r > 0 \)
\( M = \dfrac{P}{n} \quad \text{if } r = 0 \)
Total interest (no extra payments): \( I = n \cdot M - P \)
When extra payment \( E \) is applied monthly, principal is reduced faster. We simulate each month:
\( \text{Interest}_t = B_{t-1} \cdot r,\quad \text{Principal}_t = \min\!\left(M + E - \text{Interest}_t,\; B_{t-1}\right) \)
\( B_t = \max\!\left(B_{t-1} - \text{Principal}_t,\; 0\right) \)
Glossary of Variables
- P (Principal): Amount financed. If the origination fee is financed, it is added to P; if paid upfront, P is the loan amount and fee is deducted from cash received.
- APR: Annual Percentage Rate. Yearly cost of credit; monthly periodic rate is r = APR/12.
- r: Monthly periodic rate used for interest accrual each period.
- n: Number of monthly payments (term in months).
- M: Scheduled monthly payment computed by the amortization formula (excludes optional extra E).
- E: Extra monthly payment applied directly to principal.
- Total Interest: Sum of all interest charges over the life of the loan.
- Total Cost: Total of payments plus any financed fee.
- Net Disbursed: Cash received by the borrower after any upfront fee deduction.
How It Works: A Step-by-Step Example
Suppose you borrow $10,000 at 11% APR for 36 months with a 5% origination fee paid upfront, and you add an extra $50 each month.
- Fee amount = 5% × $10,000 = $500. Net disbursed = $9,500. Principal P = $10,000 (fee not financed).
- Monthly rate r = 11% / 12 = 0.9167% ≈ 0.009167.
- Monthly payment M = P × r / (1 − (1 + r)^(−n)).
- Without extras, total interest I = n × M − P.
- With an extra E = $50 monthly, iterate month-by-month reducing the balance faster until it reaches 0. You’ll pay off earlier and save interest.
Frequently Asked Questions (FAQ)
Is APR the same as the interest rate?
No. APR reflects the cost of credit including certain fees, while a nominal rate may exclude them. This tool follows the monthly periodic rate approach aligned with Regulation Z.
Why does the last payment differ when extra payments are used?
Extra principal can cause the final scheduled payment to be smaller than usual because the remaining balance becomes minimal before the end of the original term.
What if I finance the origination fee?
The fee is added to the principal, increasing the payment and total interest, but the net cash you receive is not reduced.
Does this calculator consider payment dates within a month?
It assumes equal monthly periods and end-of-period payments. Day-count conventions and mid-cycle disbursements are outside the scope.
Can my lender charge a prepayment penalty?
Some loans include prepayment penalties. Always check your loan agreement. This tool assumes no prepayment penalties.
How accurate are these estimates?
They are mathematically precise for the stated assumptions. Real-world results may differ due to compounding conventions, fees, or payment timing.
Will this affect my credit score?
No. This is an educational calculator. It does not run a credit check or affect your credit profile.