Data Source and Methodology

This calculator determines the monthly payment for a fixed-rate amortizing loan and computes the Annual Percentage Rate (APR) based on the loan's interest rate and financed origination fees.

The methodology for calculating APR strictly adheres to the standards set by the U.S. Truth in Lending Act (Regulation Z). This regulation ensures that the advertised cost of credit is transparent and uniform, allowing consumers to accurately compare different loan offers.

• Authoritative Source: U.S. Consumer Financial Protection Bureau (CFPB)
• Reference: 12 C.F.R. Part 1026 (Regulation Z)
• Link: consumerfinance.gov/rules-policy/regulations/1026/

All calculations are based rigorously on the formulas derived from this source.

The Formulas Explained

The calculator first determines your fixed monthly payment (M) using the standard amortization formula.

It then calculates the APR, which is the "true" annual cost of your loan. The APR is the interest rate that makes the present value of all your monthly payments equal to the amount you actually received (the loan amount *minus* the origination fees).

Where the calculator solves for $i$ (the periodic APR) and then multiplies by 12 to get the annual APR.

Glossary of Variables

Loan Amount (P)

The total principal amount you are borrowing.

Annual Interest Rate (Note Rate)

The stated interest rate of the loan, used to calculate interest payments. This is *not* the APR.

Loan Term (n)

The total number of payments (e.g., 3 years = 36 monthly payments).

Monthly Interest Rate (r)

The annual rate divided by 12.

Origination Fee

A one-time fee charged by the P2P platform to process your loan. This fee is subtracted from your loan amount, but you still pay interest on the full amount.

Net Proceeds

The cash you actually receive: Loan Amount - Origination Fee.

Monthly Payment (M)

The fixed amount you pay each month, which includes both principal and interest.

Effective APR (i)

The Annual Percentage Rate. This is the true, effective cost of your loan, expressed as an annual rate, because it accounts for the origination fee. It will always be higher than your Note Rate if a fee is charged.

How It Works: A Step-by-Step Example

Let's walk through a realistic scenario:

• Loan Amount: $10,000
• Annual Interest Rate: 7.5%
• Loan Term: 3 Years (36 months)
• Origination Fee: 3% ($300)

1. Calculate Monthly Payment: First, we find the payment based on the full $10,000.
   • $P = 10000$
   • $r = 0.075 / 12 = 0.00625$
   • $n = 36$
   • Using the formula $M = P \frac{r(1+r)^n}{(1+r)^n - 1}$, the Monthly Payment (M) is $311.06.
2. Calculate Net Proceeds: You don't receive the full $10,000.
   • $10,000 (Loan) - $300 (Fee) = $9,700. You only get $9,700 in cash.
3. Calculate APR: The calculator now finds the interest rate that makes 36 payments of $311.06 equal to a present value of $9,700.
   • This calculation reveals an Effective APR of 9.516%.

As you can see, while your "note rate" was 7.5%, the 3% fee increased the *true cost* of your loan to over 9.5%. This is why comparing loans by APR, not just interest rate, is essential.

M = P \frac{r(1+r)^n}{(1+r)^n - 1}

\text{Net Proceeds} = \sum_{k=1}^{n} \frac{M}{(1 + i)^k}

$ M = P \frac{r(1+r)^n}{(1+r)^n - 1} $

$ \text{Net Proceeds} = \sum_{k=1}^{n} \frac{M}{(1 + i)^k} $