Mark Jensen is a CPA with expertise in consumer credit regulation and TILA compliance, ensuring calculations reflect the true Annual Percentage Rate.
Use the authoritative **Annual Percentage Rate Calculator** to find the true cost of borrowing, including interest. Enter any three variables—Loan Principal, Term in Months, Monthly Payment, or APR—to solve for the remaining unknown value.
Annual Percentage Rate Calculator
APR Formula
The calculation is based on the Amortization formula, solved iteratively:
$$\mathbf{M} = \mathbf{P} \frac{\mathbf{i}(1 + \mathbf{i})^{\mathbf{n}}}{(1 + \mathbf{i})^{\mathbf{n}} – 1}$$
Where $\mathbf{i} = \mathbf{APR} / 1200$ (Monthly Rate)
$$\mathbf{APR} = \mathbf{i} \times 1200$$
Solving for APR (Q) requires finding the monthly rate $\mathbf{i}$ that makes the equation balance.
Formula Source: Investopedia (Amortization Formula)Formula Variables
- F ($\mathbf{P}$): Loan Principal. The initial amount borrowed.
- P ($\mathbf{n}$): Loan Term in Months. The total number of payments.
- V ($\mathbf{M}$): Monthly Payment. The fixed amount paid each month.
- Q ($\mathbf{APR}$): Annual Percentage Rate. The standardized cost of the loan (%).
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What is the Annual Percentage Rate (APR)?
The Annual Percentage Rate (APR) is the annual rate charged for borrowing funds, expressed as a single percentage number. Unlike the simple interest rate, the APR is intended to represent the true yearly cost of the loan over its term, as it often includes mandatory fees and costs (though in simple amortization, it is largely the interest rate). Its purpose, as mandated by the Truth in Lending Act (TILA) in the US, is to provide consumers with a standardized metric for comparing loans.
Crucially, APR is calculated before taking into account the effects of compounding, making it the **Nominal Rate**. The rate that *does* include compounding is the Effective Annual Rate (EAR). For a loan where interest is compounded monthly, the EAR will be slightly higher than the stated APR. This calculator uses the loan’s principal, term, and payment to determine the interest rate (APR) that makes the loan balance, based on the standard amortization formula.
How to Calculate Required Monthly Payment (Example)
Let’s find the required Monthly Payment ($\mathbf{M}$, V) for a Loan Principal ($\mathbf{P}$, F) of \$20,000, a Term ($\mathbf{n}$, P) of 48 months, and an APR ($\mathbf{APR}$, Q) of 5.5\%.
- Step 1: Calculate Monthly Interest Rate ($\mathbf{i}$)
Monthly Rate ($\mathbf{i}$) = $5.5\% / 1200 = 0.0045833$.
- Step 2: Apply the Monthly Payment Formula
Using the amortization formula: $\mathbf{M} = P \frac{i(1 + i)^n}{(1 + i)^n – 1}$
- Step 3: Substitute and Solve for $\mathbf{M}$
The calculation yields a required Monthly Payment ($\mathbf{M}$, V) of **\$464.67**.
Frequently Asked Questions (FAQ)
The APR is often very close to the interest rate, but it is technically a broader measure. The interest rate is simply the cost of borrowing the principal. APR is the interest rate plus any fees charged by the lender (though this calculator focuses on the rate required to satisfy the amortization parameters).
How does APR affect my loan?The APR directly determines how much total interest you will pay over the life of the loan. A higher APR means a higher monthly payment and a much larger total cost for the same principal amount and term.
What is the difference between APR and EAR/APY?APR is the *stated* annual rate (nominal), ignoring compounding effects (or assuming simple interest). EAR/APY is the *effective* annual rate, which is the true yield/cost after accounting for interest compounding over the year. EAR is a more accurate measure of a loan’s true cost.
Can I calculate a loan’s APR if I don’t know the fees?Yes, but the result will be the ‘nominal rate’ that satisfies the principal, term, and payment. To get the official, legally defined APR (which includes fees), you must know the fees and adjust the principal amount used in the amortization formula accordingly.