APR Calculator Mortgage

APR Equation:

\[ PV = \sum_{t=1}^{n} \left( \frac{PMT}{(1 + APR/12)^t} \right) - Fees \]

Loan Amount (PV):

USD

Monthly Payment (PMT):

USD

Loan Term:

years

Closing Costs (Fees):

USD

Annual Percentage Rate (APR):

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1. What is APR?

The Annual Percentage Rate (APR) is the true cost of borrowing, including both interest rate and certain fees. It provides a more comprehensive measure of loan cost than the interest rate alone, making it easier to compare different loan offers.

2. How Does the Calculator Work?

The calculator uses the following equation to solve for APR:

\[ PV = \sum_{t=1}^{n} \left( \frac{PMT}{(1 + APR/12)^t} \right) - Fees \]

Where:

\( PV \) — Loan amount (present value)
\( PMT \) — Monthly payment
\( APR \) — Annual percentage rate (decimal)
\( t \) — Month number (1 to n)
\( n \) — Total number of months (term × 12)
\( Fees \) — Closing costs

Explanation: The equation balances the loan amount plus fees against the present value of all future payments. The calculator solves this iteratively using the Newton-Raphson method.

3. Importance of APR Calculation

Details: APR helps borrowers compare loans with different interest rates and fee structures. It's particularly important for mortgages where closing costs can vary significantly between lenders.

4. Using the Calculator

Tips: Enter the loan amount, monthly payment, loan term in years, and any closing costs. All values must be positive numbers. The calculator will solve for the APR that makes the equation balance.

5. Frequently Asked Questions (FAQ)

Q1: Why is APR different from interest rate?
A: APR includes both the interest rate and certain fees, giving a more complete picture of borrowing costs.

Q2: What fees are included in APR?
A: Typically includes origination fees, points, mortgage insurance, and some closing costs, but not all fees (like appraisal or title insurance).

Q3: Why does my APR seem high compared to interest rate?
A: This usually indicates significant upfront fees. The more fees included, the higher the APR will be relative to the interest rate.

Q4: Are there limitations to APR?
A: APR assumes you'll keep the loan for its full term. If you plan to refinance or sell soon, APR may not accurately reflect your costs.

Q5: How accurate is this calculator?
A: It provides a good estimate, but actual APR calculations may vary slightly based on lender-specific methodologies.