APR Calculator

APR is evaluated from Loan Amount, Stated Interest Rate and Loan Term. The calculation reports Monthly Payment, True APR and Rate vs APR Spread.

Results

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About the APR Calculator

APR is treated here as a quantitative relation between Loan Amount, Stated Interest Rate, Loan Term and Total Fees & Closing Costs and Monthly Payment, True APR and Rate vs APR Spread.

The calculator uses a custom php logic configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
APR is calculated by finding the discount rate that makes the present value of all payments equal to the net proceeds (loan amount minus fees).
Net Proceeds = Loan Amount - Fees
Monthly Payment = same as standard amortization at stated rate
APR = rate (r) such that:
Net Proceeds = Payment x [1 - (1+r)^ - n] / r
This requires an iterative Newton-Raphson or bisection solve (not a closed-form formula).

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

APR is calculated by finding the discount rate that makes the present value of all payments equal to the net proceeds (loan amount minus fees).
Net Proceeds = Loan Amount - Fees
Monthly Payment = same as standard amortization at stated rate
APR = rate (r) such that:
Net Proceeds = Payment x [1 - (1+r)^ - n] / r
This requires an iterative Newton-Raphson or bisection solve (not a closed-form formula).

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Standard Mortgage APR

Inputs

loan_amount: 350000 stated_rate: 6.75 loan_months: 360 fees: 7000
Monthly Payment: $2,270.09. True APR: 6.948%. Rate vs APR Spread: 0.198%

With Loan Amount = 350,000, Stated Interest Rate = 6.75, Loan Term = 360 and Total Fees & Closing Costs = 7,000 as the stated inputs, the result is Monthly Payment = $2,270.09, True APR = 6.948% and Rate vs APR Spread = 0.198%. Each value corresponds to the declared output fields.

Example 2: High-Fee Low-Rate Offer

Inputs

loan_amount: 300000 stated_rate: 6.25 loan_months: 360 fees: 12000
Monthly Payment: $1,847.15. True APR: 6.641%. Rate vs APR Spread: 0.391%

With Loan Amount = 300,000, Stated Interest Rate = 6.25, Loan Term = 360 and Total Fees & Closing Costs = 12,000 as the stated inputs, the result is Monthly Payment = $1,847.15, True APR = 6.641% and Rate vs APR Spread = 0.391%. Each value corresponds to the declared output fields.

Example 3: Short-Term Personal Loan

Inputs

loan_amount: 10000 stated_rate: 12 loan_months: 36 fees: 400
Monthly Payment: $332.14. True APR: 14.863%. Rate vs APR Spread: 2.863%

With Loan Amount = 10,000, Stated Interest Rate = 12, Loan Term = 36 and Total Fees & Closing Costs = 400 as the stated inputs, the result is Monthly Payment = $332.14, True APR = 14.863% and Rate vs APR Spread = 2.863%. Each value corresponds to the declared output fields.

Example 4: No Fees — APR Equals Rate

Inputs

loan_amount: 25000 stated_rate: 9.99 loan_months: 60 fees: 0
Monthly Payment: $531.05. True APR: 9.99%. Rate vs APR Spread: 0%

With Loan Amount = 25,000, Stated Interest Rate = 9.99, Loan Term = 60 and Total Fees & Closing Costs = 0 as the stated inputs, the result is Monthly Payment = $531.05, True APR = 9.99% and Rate vs APR Spread = 0%. Each value corresponds to the declared output fields.

Common Use Cases

  • Find the true APR of a mortgage including all fees
  • Compare loan offers on an apples-to-apples APR basis
  • Understand how fees affect the effective cost of borrowing