Factor Rate to APR Calculator
Result:
What is Factor Rate and APR?
A factor rate is a method used by some lenders to calculate loan payments, particularly in the small business lending space. It's a flat rate applied to the initial amount borrowed to determine the total repayment amount. For example, a factor rate of 0.02 means you'll repay $1.02 for every $1.00 borrowed.
APR (Annual Percentage Rate), on the other hand, represents the true annual cost of borrowing, taking into account not just the interest rate but also any fees associated with the loan, expressed as a yearly percentage. It's a more standardized way to compare the cost of different loan products.
This calculator helps you convert a factor rate into an equivalent APR. This is useful for understanding the true annual cost of a loan offered with a factor rate and for comparing it to loans that use a traditional APR structure. The conversion accounts for the loan term, as a shorter term with the same factor rate will result in a higher APR.
How the Calculation Works:
The formula to convert a factor rate to APR involves understanding that the total repayment is the principal plus the total cost of the loan. The factor rate determines this total cost relative to the principal. We then express this cost on an annual basis over the loan's term.
Let:
F= Factor RateT= Loan Term in MonthsP= Principal Loan Amount (Note: The principal amount cancels out in the APR calculation, making the conversion independent of the loan size.)
The total repayment amount per payment period is typically calculated as:
Repayment per Period = Principal * Factor Rate
However, the factor rate usually represents the total repayment multiplier. A more common interpretation is:
Total Repayment = Principal * (1 + Factor Rate)
Or, the factor rate is directly the multiplier for the total repayment (e.g., 1.02 means $1.02 repaid for every $1.00 borrowed). Assuming the latter interpretation for simplicity in conversion to APR:
Total Repayment = Principal * Factor Rate (as multiplier, e.g. 1.02)
Total Cost of Loan = Total Repayment - Principal = Principal * (Factor Rate - 1)
Cost Per Month = Total Cost of Loan / Loan Term = (Principal * (Factor Rate - 1)) / T
To express this as an APR, we need to find the equivalent annual interest rate. The formula is derived from the loan amortization formula. A simplified, common approximation for converting factor rate to APR is:
APR = (Factor Rate - 1) * 24 (This is a very rough approximation for short-term, high-cost loans and not universally accurate. A more precise method involves iterative calculations or the effective interest rate formula, but for a simple calculator, we'll use a commonly cited conversion that approximates the annual cost.)
A more widely accepted and accurate formula, treating the factor rate as a multiplier for the total repayment over the term, is:
APR = ((Factor Rate - 1) / Loan Term (in years)) * 100%
Let's refine this to a more robust calculation that approximates the effective rate.
The total amount to be repaid is `Principal * Factor Rate`.
The total interest paid is `(Principal * Factor Rate) – Principal = Principal * (Factor Rate – 1)`.
The monthly interest paid is `Principal * (Factor Rate – 1) / Loan Term (in months)`.
The monthly payment is `(Principal * Factor Rate) / Loan Term (in months)`.
The APR can be approximated by considering the total interest paid over the loan term relative to the average outstanding balance.
A common and practical approximation for converting a factor rate (F) over a term (T in months) to an APR is:
APR = (F - 1) * (24 if T=60, or adjust based on term)
A more precise calculation often involves financial functions or iterative methods. For this calculator, we will use the following commonly accepted approximation which better reflects the annual cost:
APR = ((Factor Rate - 1) / (Loan Term in Months / 12)) * 100
This formula calculates the total cost as a percentage of the principal, annualizes it by dividing by the loan term in years, and then multiplies by 100 to get a percentage.