Mortgage APR Calculator
Calculate the Annual Percentage Rate (APR) for your mortgage. Compare your nominal interest rate against the APR including upfront closing costs and points.
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What is Mortgage APR?
The Annual Percentage Rate (APR) is a broader measure of the cost of borrowing money than the nominal interest rate. While your interest rate determines the size of your monthly principal and interest payment, the APR reflects the total cost of the loan by incorporating both the interest rate and any upfront closing fees charged by the lender (such as origination fees, discount points, processing fees, and private mortgage insurance).
Federal law (Truth in Lending Act) requires lenders to disclose the APR on your loan estimate to help you compare loan offers fairly. Because some lenders may offer a lower interest rate but charge higher upfront fees, comparing loans based on their interest rate alone can be misleading. Comparing APRs provides a truer picture of the loan cost. This mortgage APR calculator makes it easy to calculate and compare APRs.
How Mortgage APR is Calculated
Calculating the APR requires solving for the internal rate of return (IRR) of the loan cash flows. Effectively, we find the interest rate that makes the present value of all monthly payments equal to the net loan proceeds (loan amount minus upfront lender fees):
\[\text{Net Loan Proceeds} = \sum_{t=1}^{N} \frac{PMT}{(1 + i_{APR})^t}\]Where:
- \(\text{Net Loan Proceeds}\) = Loan amount minus upfront lender closing costs and points
- \(PMT\) = Monthly payment calculated using the nominal interest rate
- \(i_{APR}\) = Monthly APR rate (annual APR divided by 12)
- \(N\) = Total number of monthly payments
This equation cannot be solved algebraically; instead, our calculator uses a numerical binary search algorithm to find the exact APR rate.
Step-by-Step APR Calculation Example
Imagine you purchase a home for $380,000 with a $76,000 down payment (20% down). Your loan amount is $304,000 at a nominal interest rate of 6.5%, and you pay $5,500 in upfront lender fees:
- Calculate Net Loan Proceeds: \(304,000 - 5,500 = \mathbf{\$298,500}\).
- Calculate Monthly P&I Payment: At 6.5% over 30 years, your payment is $1,921.49.
- Solve for APR: We find the interest rate that equates 360 payments of $1,921.49 to a net loan of $298,500. The resulting annual APR rate is 6.671%.
- Comparison: The APR is 0.171% higher than your nominal rate of 6.50%, representing the amortization of the $5,500 fee over the 30-year term.
Frequently Asked Questions (FAQ)
What is the difference between interest rate and APR?
The interest rate is the percentage you pay to borrow the principal balance. The APR (Annual Percentage Rate) includes both this interest rate and any upfront fees (like points, origination fees) charged by the lender, expressing the total cost as an annual percentage.
Why is the APR higher than my interest rate?
The APR is higher because it incorporates upfront closing costs and fees in addition to the base interest rate. If a lender charged zero fees, your APR would equal your nominal interest rate.
Which fees are included in the APR?
Fees included in the APR are origination fees, discount points, processing fees, underwriting fees, private mortgage insurance (PMI), and prepaid interest. Fees like appraisal, title insurance, and credit checks are typically excluded.
Is a lower APR always better?
Not necessarily. If you plan to stay in the home for only a few years, a loan with a lower interest rate and higher fees (yielding a higher APR) might actually be cheaper because you won't hold the loan long enough to justify the upfront fees. APR assumes you hold the loan for the full term.
How do discount points affect APR?
Discount points are prepaid interest paid at closing to lower your nominal rate. Because they are an upfront fee, buying points increases your APR relative to your interest rate, but it will lower both if you stay in the home long enough.
Does down payment affect APR?
A larger down payment does not directly change the APR formula, but it can lower your APR by eliminating the need for Private Mortgage Insurance (PMI), which is a significant fee included in the APR.
How is APR disclosed to home buyers?
APRs are disclosed on the official Loan Estimate (LE) document provided by your lender within three days of applying for a mortgage, and again on the Closing Disclosure (CD) before signing final papers.
What is the APR on an adjustable-rate mortgage (ARM)?
For ARMs, the APR is calculated based on the initial fixed interest rate for the initial term, and then projects future rate adjustments based on current market index values. It is only an estimate.
Why do some lenders advertise low rates but high APRs?
Lenders advertise low nominal interest rates to attract buyers, but they may offset this by charging high origination fees or requiring you to buy discount points. Checking the APR exposes these hidden upfront costs.
Can APR help me compare conventional and FHA loans?
Yes. FHA loans have low rates but require both upfront and monthly MIP fees. Comparing the APR of FHA loans against conventional loans is the best way to see which program is truly cheaper overall.