Data Source and Methodology
Authoritative Data Source: Consumer Financial Protection Bureau (CFPB), Regulation Z (Truth in Lending Act), 12 CFR 1026, Appendix J — Annual Percentage Rate (APR) calculations for closed-end credit (last revised 2023-10-01). Read Appendix J. All calculations strictly follow standard amortization mathematics and periodic compounding aligned to the payment frequency.
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formula Explained
Let:
• L = principal financed (including any financed origination fee),
• r = periodic rate = APR / m, where APR is nominal (as a decimal) and m is payments per year,
• n = total number of payments.
Scheduled payment for a fully amortizing loan:
$$ P = \frac{r \cdot L}{1 - (1+r)^{-n}} \quad \text{for } r > 0 \quad ; \quad P = \frac{L}{n} \text{ if } r = 0 $$
Effective Annual Rate (from periodic compounding):
$$ \text{EAR} = (1 + r)^{m} - 1 $$
Balance recurrence (each period t):
$$ I_t = r \cdot B_{t-1}, \quad \text{Principal}_t = P^\* - I_t, \quad B_t = B_{t-1} - \text{Principal}_t $$
where \( P^\* = P + \text{Extra} \) when extra payments are used; the final payment is adjusted to avoid overpaying.
Glossary of Variables
- Loan amount: Amount borrowed before fees.
- APR (nominal): Annual rate not including fees; used to compute the periodic rate.
- Payment frequency: Number of payments per year (12 monthly, 26 biweekly, 52 weekly).
- Origination fee: Percentage of loan; financed means added to principal; otherwise paid upfront.
- Other upfront fees: Flat amounts paid at closing, not financed.
- Extra payment: Additional amount paid every period on top of the scheduled payment.
- Payment per period: Scheduled payment before any extra.
- Number of payments: Count required to fully amortize the loan (shorter if extra payments are made).
- Total interest: Sum of interest across all periods.
- Total fees: Origination (percent) + other fees.
- Total cost: Total interest + total fees.
- Net funds to business: Loan amount minus upfront fees.
- Effective Annual Rate (EAR): Annualized rate reflecting compounding at the selected frequency.
How It Works: A Step-by-Step Example
Suppose a business borrows $100,000 at 9% APR for 5 years with monthly payments. An origination fee of 2% is paid upfront, plus $500 in other fees. An extra $100 is added to each payment.
- Payments per year m = 12; total payments n = 5 × 12 = 60; periodic rate r = 0.09 / 12 = 0.0075.
- Financed principal L = 100,000 (fee is upfront, not financed).
- Scheduled payment: \( P = \frac{0.0075 \cdot 100000}{1 - (1.0075)^{-60}} \approx 2076.75 \).
- With extra = 100, pay \( P^\* = 2176.75 \) each month until balance reaches 0; the last payment is smaller.
- Total fees = 2,000 + 500 = 2,500; Net funds = 100,000 − 2,500 = 97,500.
- The calculator iterates the amortization to return actual payoff time and total interest, and compares with the baseline without extra to show savings.
Frequently Asked Questions (FAQ)
What payment frequencies are supported?
Monthly (12/year), biweekly (26/year), and weekly (52/year). Compounding is assumed to match the frequency.
Do fees affect my payment?
Financed fees increase the principal and thus the payment and interest. Upfront fees do not change the scheduled payment but reduce net funds disbursed.
Can I model extra payments?
Yes. Add an amount in “Extra payment per period.” It is applied directly to principal after interest, shortening payoff time.
What is the difference between APR and EAR?
APR is a nominal annual rate used for disclosures. EAR converts the periodic rate (APR divided by payments per year) into an effective annual rate using compounding.
Is this calculator suitable for loans with balloons or interest-only periods?
This version models level-payment amortizing loans. For balloon or interest-only structures, consult your lender’s amortization schedule or a specialized calculator.
Are my inputs saved?
As you type, the URL updates with your inputs. You can bookmark or share it to revisit the same scenario.
Does this tool provide financial advice?
No. It provides educational estimates based on standard formulas. Always verify terms with your lender and consult a qualified advisor.