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APR Calculator

The annual percentage rate (APR) folds fees into the cost of borrowing, so it is usually higher than the quoted interest rate.

Calculated Result
7.06%%

APR

Annual percentage rate (APR)

7.06%

Nominal interest rate

6%

Monthly payment

$386.66

Total interest

$3,199.36

Total repaid

$23,199.36

Net amount received

$19,500.00

Fees financed

$500.00

7.06% — APR

Calculation Breakdown

  1. Monthly payment (nominal rate)M = P·r / (1 − (1+r)⁻ⁿ) = $386.66
  2. Net proceeds$20,000.00 − $500.00 = $19,500.00
  3. Solve for the rateFind the monthly rate where the present value of payments equals the net proceeds, then multiply by 12.APR=12⋅i∗\text{APR} = 12 \cdot i^*

What Is the APR Calculator?

An APR calculator shows the true annual cost of a loan once fees are included.

How Does the APR Calculator Work?

It computes the payment at the nominal rate, then finds the rate that ties those payments to the net cash received.

APR Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

Net=∑k=1nM(1+i)k,APR=12i\text{Net} = \sum_{k=1}^{n} \dfrac{M}{(1+i)^k}, \quad \text{APR} = 12i

Fees reduce the cash you actually receive, so the same payments imply a higher rate — the APR.

How to Use the APR Calculator

  1. Enter the loan amount, interest rate, term in months and any upfront fees.

Step-by-Step Example Calculation

$20,000 at 6% for 60 months with $500 fees

Input Values:

loanAmount:20000
interestRate:6
termMonths:60
fees:500
Worked Steps: The APR is slightly above the 6% nominal rate because of the fees.

Understanding Your Result

The APR is the all-in annual cost; it sits above the nominal rate when fees apply.

Factors That Affect the Result

  • Interest rate, term, fees and loan amount all move the APR.

When Should You Use This Calculator?

  • Use it to compare loan offers fairly.

Assumptions & Limitations

  • Assumes monthly payments and ignores late fees or variable rates.

Frequently Asked Questions

Calculation Accuracy & Reference Note

This calculator implements verified, deterministic mathematical equations based on published standards. Results should be treated as professional engineering estimates; always verify critical operations with local equipment manuals and site inspections.

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