How to Calculate APR (Including Mortgage APR)

The annual percentage rate (APR) is the one number designed to let you compare loans fairly. Unlike the interest rate, it includes most of the lender’s upfront charges, so a loan that hides its cost in fees can’t look cheaper than it is. This guide explains exactly how APR is calculated, walks through a mortgage example, and shows how to check any APR in Excel.

Interest rate vs. APR

• The interest rate (or note rate) sets your monthly payment.
• The APR measures the cost of borrowing against the money you actually receive, after upfront finance charges.

If a loan has no fees, the two are equal. Every dollar of finance charges pushes the APR above the interest rate.

What counts as a finance charge?

In the US, the Truth in Lending Act decides what goes into APR. Typically included:

• Origination and underwriting fees
• Discount points
• Mortgage broker fees
• Prepaid interest
• Mortgage insurance premiums

Typically excluded, because you’d pay them in a cash purchase too:

• Appraisal and credit report fees
• Title insurance and settlement fees
• Recording fees and transfer taxes

Your Loan Estimate shows the APR and lists the charges that went into it.

How APR is calculated, step by step

1. Payment: calculate the monthly payment on the full loan at the note rate.
2. Amount financed: subtract the prepaid finance charges from the loan.
3. APR: find the rate at which the payments repay exactly the amount financed:

amount financed = payment × (1 − (1 + i)^−n) ÷ i
APR = i × 12

Step 3 has no direct algebraic solution, so lenders’ software, Excel and the APR calculator solve it numerically.

Worked example: mortgage APR

A $300,000 mortgage at 6.5% for 30 years, with $6,000 of points and origination fees.

1. Payment: $300,000 at 6.5% over 360 months = $1,896.20.
2. Amount financed: 300,000 − 6,000 = $294,000.
3. APR: the monthly rate that makes 360 payments of $1,896.20 worth $294,000 is 0.5579%, so the APR is 6.695%.

The fees add 0.195 points to the rate. Spread over a shorter period, they matter more. The same loan and fees over 7 years would give an APR of 7.122%. That is why short-term loans with fees often have surprisingly high APRs. To see the full monthly housing cost, including tax and insurance, use the mortgage calculator.

Calculating APR by hand: trial and error

Without software, you can still find the APR by testing rates until the payments’ present value matches the amount financed:

1. Try 6.6%: 360 payments of $1,896.20 discounted at 6.6% ÷ 12 are worth $296,904.08. That is too high, so the rate must be higher.
2. Try 6.7%: they are worth $293,858.48. That is too low, so the rate is between 6.6% and 6.7%.
3. Narrow it down: $294,000 sits about 95% of the way from $296,904 to $293,858, so try 6.695%. That gives $294,009.58, within a few dollars of the target.

Each step is a present value calculation, so a finance calculator speeds it up. In practice, lenders and spreadsheets automate exactly this search.

How to calculate APR in Excel

Use PMT for the payment, then RATE for the APR:

=PMT(6.5%/12, 360, -300000)                 → 1,896.20
=RATE(360, -1896.20, 294000) * 12          → 6.695%

Or in one formula:

=RATE(360, PMT(6.5%/12,360,-300000), -(300000-6000)) * 12

If you only know the payment and the amount you received, RATE alone is enough. For example, *=RATE(36,-330,10000)12 gives 11.55% for a $10,000 loan at $330 a month for 3 years. The interest rate calculator does the same without a spreadsheet.

Monthly APR and daily periodic rate

• Monthly rate: APR ÷ 12. An APR of 6.695% is 0.5579% a month.
• Credit cards charge interest daily using the daily periodic rate, APR ÷ 365. A card at 24.99% APR charges about 0.0685% a day on your balance.

APR on different kinds of credit

• Mortgages: the APR includes points and lender fees, as in the example above. The Loan Estimate must show it on page 3.
• Personal loans: origination fees of 1–8% are common, and they are often taken out of the money you receive. A $20,000 loan at 8% with a $600 fee has an APR of about 9.3%.
• Credit cards: with no upfront fee, the APR equals the stated rate. Interest is charged daily on the average balance, and cash advances often carry a higher APR.
• Payday loans: fees are quoted per $100 borrowed. A $15 fee per $100 for a 14-day loan is an APR of 15 ÷ 100 × 365 ÷ 14 = 391%. This is exactly the kind of cost APR was designed to expose.
• Buy now, pay later and store financing: check whether “0%” plans charge deferred interest if the balance isn’t cleared in time.

How to get a lower APR

1. Improve your credit score before applying. Even a small improvement can move you into a better pricing tier.
2. Compare at least three offers for the same loan type and term, using each lender’s APR.
3. Negotiate the fees. Origination and processing fees are often negotiable, and every dollar removed lowers the APR.
4. Weigh points carefully. Buying points lowers the rate and usually the APR, but only pays off if you keep the loan long enough.
5. Choose a shorter term if you can afford it. Rates on shorter loans are often lower.

APR vs. APY

APR doesn’t include compounding. APY (annual percentage yield) does, and it is used for savings. A loan’s effective annual cost is a little higher than its APR when interest compounds monthly. To convert between rate types, solve with the finance calculator.

Common mistakes when comparing APRs

• Comparing different terms. A 15-year and a 30-year APR aren’t directly comparable.
• Ignoring how long you’ll keep the loan. APR assumes the full term. If you’ll refinance in five years, points you paid upfront are spread over far fewer payments than the APR assumes.
• Adding non-finance fees. Including title or appraisal costs inflates your own APR calculation.
• Assuming APR is fixed on adjustable-rate loans. An ARM’s APR is an estimate based on today’s index values.
• Comparing APR with APY. Make sure both offers quote the same kind of rate.
• Ignoring closing costs outside the APR. Title and appraisal fees don’t change the APR, but they still come out of your pocket. Compare the Loan Estimate’s “cash to close” as well.

Frequently asked questions

What is the formula for APR?

APR is the yearly rate that makes the loan payments worth exactly the amount you actually receive (the loan minus upfront finance charges). Solve amount financed = payment × (1 − (1 + i)^−n) ÷ i for i, then APR = i × 12. There is no direct formula, so it is solved numerically.

How do I calculate APR from a monthly payment?

Use the amount you received, the payment and the number of payments. In Excel, =RATE(36,-330,10000)*12 gives 11.55% for a $10,000 loan repaid at $330 a month for 36 months.

How do I convert APR to a monthly rate?

Divide by 12. An APR of 6.695% is 0.5579% a month. For credit cards, the daily periodic rate is the APR ÷ 365, so 24.99% APR is about 0.0685% a day.

Why is the APR on my Loan Estimate higher than the rate?

Because it includes finance charges such as origination fees and discount points. On a $300,000 loan at 6.5% with $6,000 of such fees, the APR is 6.695%.

Is a lower APR always better?

For the same loan type and term, usually yes. But APR assumes you keep the loan for its full term. If you'll sell or refinance in a few years, a loan with lower upfront fees can be cheaper even with a slightly higher APR.