How to calculate APR: Formula, examples, and step-by-step guide

Interest rates. Closing costs. Lender fees. All of these play a factor in understanding the true cost of a loan. That’s why understanding an Annual Percentage Rate (APR) is so important for borrowers. It provides a more accurate and complete picture of the total cost of a loan compared to just looking at the interest rate.

So how does the APR formula work? In this guide, we’ll outline how to calculate APR, examples for different loan types, and how lenders implement accurate APR calculations.

What is APR? (and how it differs from interest rate)

Interest rates are just one piece of the puzzle when it comes to the total cost of a loan. For a more complete view for borrowers comparing loan costs, an APR provides the annualized cost of a loan, inclusive of all fees like origination, closing costs, or mortgage points. While both are shown as a percentage, there is a big difference between APR and interest rate:

• Interest rate is the base percentage charged on the principal amount borrowed.
• APR includes the interest rate plus any lender fees, insurance, and closing costs.

While a lower interest rate may look appealing at face value, the loan may actually cost more in the long run because of significant fees. The APR acts as a standard for comparing the true cost of loans because any fees aren’t hidden in the paperwork. The Truth in Lending Act (TILA) ensures it: lenders must properly calculate and disclose the Annual Percentage Rate. This is part of Regulation Z for companies in the United States, which creates standardized requirements for how credit providers disclose terms to consumers.

You simply can’t compare loans on interest rates alone.

The APR formula explained

Here are the steps to calculate an APR:

1. Sum of finance charges: Add up all of the interest and fees to be paid over the life of the loan.
2. Divide by the loan principal amount borrowed: Divide the sum total interest and fees by the loan principal amount.
3. Determine daily interest rate: Then, you divide that resulting amount by the number of days in the loan term to calculate the daily interest rate.
4. Calculate the annual rate: Multiply the daily rate by 365 to get the annual rate.
5. Convert to a percentage: Multiply the annual rate amount by 100 to determine the APR percentage.

APR calculation formula

APR = ((Interest + Fees / Loan Amount) / Number of Days in Loan Term) × 365 × 100

Step-by-step guide to calculate APR

Now that we’ve explained the basic APR calculation formula, let’s walk through a step-by-step example of the calculation process.

Let’s assume a borrower is evaluating a $10,000 loan over a 3-year term. The details of the loan are as follows:

• Loan amount: $10,000
• Annual interest rate: 8%
• Loan term: 3 years (1,095 days)
• Origination fee: $300
• Total interest paid: $2,400 (Loan amount x Annual interest rate x Loan term)

Following the steps outlined above, the calculation would result in a 8.97% APR:

Calculating simplified APR

Total interest and fees: $2,400 + $300 = $2,700

Divide by principal: $2,700 / $10,000 = 0.27

Divide by days in term: 0.27 / 1,095 = 0.000246

Multiply by 365: 0.000246 × 365 = 0.0897

Multiply by 100: 0.0897 × 100 = 8.97% APR

By comparison, what if the same loan had no fees? In that case, the APR is the same as the interest rate. Here is how the calculation looks for a loan with no fees:

Calculating APR for loans with no fees

Total interest: $2,400 = $2,400

Divide by principal: $2,400 / $10,000 = 0.24

Divide by days in term: 0.24 / 1,095 = 0.000219

Multiply by 365: 0.000219 × 365 = 0.0799

Multiply by 100: 0.0799 × 100 = 8.00% (Rounded)

This is a simplified calculation for anyone evaluating loans based on APRs or interest rates. As you can see, the APR is nearly a full percentage point higher than the interest rate alone.

In the real world, calculations could also account for irregular payment periods, such as payment schedules that don’t follow a standard, consistent schedule.

In addition, the above and following examples assume a simple interest rate each year and are not amortized based on the present value of the loan each year. In reality, calculating amortized payments is much more complicated.

Simple interest vs. amortized interest

To calculate interest using amortization, you need to figure out how much interest you will pay each month based on the present value of the loan. For instance, you’ll pay higher interest at the beginning of a loan term when the total amount is at a higher balance. To manually calculate amortized interest, you can follow these steps:

1. Determine monthly loan payment amount: Divide the interest rate by the number of payments you’ll make that year. If you have an 8 percent interest rate, you would divide 0.08 by 12 to get 0.0067.
2. Figure out month-by-month interest total: Multiply that number by your remaining loan balance to find out how much you’ll pay in interest that month. If you have a $10,000 loan balance, your first month of interest would be $67.
3. Determine next month’s loan present value (PV): Subtract the interest amount from the monthly payment total to see how much of the principal loan will be paid. Then, subtract that amount towards the principal loan from the total loan value. This gives you the new remaining loan balance for the next month.
4. Repeat calculations and add up total interest paid: Continue this process with the remaining loan balance for each subsequent month. Add all of the interest payments together to determine the total interest paid for the life of the loan.

Examples of APR calculations by loan type

Different loan types typically include different types of fees, which changes how APR works across different lending products. Let’s look at some examples of APR calculations for different types of loans using simple interest.

Auto loan APR calculation

Auto loans typically include a number of fees to cover origination, document processing, and vehicle title and registration fees. Here’s an example of how to calculate APR on a car loan, assuming it is for $25,000 with an interest rate of 6% over 5 years and typical dealer fees:

Total interest and fees: $7,500 + $774 = $8,274

Divide by principal: $8,274 / $25,000 = 0.33

Divide by days in term: 0.33 / 1,825 = 0.00018

Multiply by 365: 0.00018 × 365 = 0.0657

Multiply by 100: 0.0657 × 100 = 6.57% APR

Personal loan APR calculation

Personal loans primarily include an origination fee equal to 1% to 10% of the loan amount. Here’s an example for a $15,000 personal loan with an interest rate of 9% over 3 years and an origination fee of 5% of the principal loan amount:

Total interest and fees: $4,050 + $750 = $4,800

Divide by principal: $4,800 / $15,000 = 0.32

Divide by days in term: 0.32 / 1,095 = 0.000292

Multiply by 365: 0.000292 × 365 = 0.1066

Multiply by 100: 0.1066 × 100 = 10.66% APR

Mortgage APR calculation

Mortgage loans involve multiple types of closing costs and can become extremely complex if they involve mortgage points or private mortgage insurance (PMI). Here’s an example for a simplified mortgage APR calculation for a 30-year mortgage at $300,000 with a 6% interest rate and multiple closing costs:

Total interest and fees: $540,000 + $10,500 = $550,500

Divide by principal: $550,500 / $300,000 = 1.835

Divide by days in term: 1.835 / 10,950 = 0.000168

Multiply by 365: 0.000168 × 365 = 0.06132

Multiply by 100: 0.06132 × 100 = 6.13% APR

Credit card APR calculation

Unlike other types of loans, credit cards don’t often have any additional fees. So, the APR is equal to the interest rate, as shown in our no fees example above.

However, there can be some credit cards that offer a variable APR vs. a fixed APR. This means that instead of a set APR for the entire life of the credit card, the interest rate changes over time based on market conditions.

The other thing to note with credit cards is that interest only accrues if the balance is not paid before a certain time. The easiest way to avoid paying interest on a credit card is to pay the balance in full each billing period.

What's considered a good APR?

Good APRs range can vary by loan type, market conditions, and a borrower’s credit worthiness. Here’s a quick cheat sheet of general benchmarks on what constitutes a good APR, factors that may affect your ability to qualify for a particular APR, and how you can qualify for the best APR.

General APR benchmarks by loan type

Factors that may affect your APR

• Credit score: This is often one of the most significant factors. The higher the score, the better rate you can secure.

• Debt-to-income (DTI) ratio: This shows how your monthly debt payments stack up against your income. A high DTI creates more risk for the lenders and could result in a higher APR.

• Type of loan and collateral: Loans that are backed by assets, such as a mortgage or car loan, often have lower APRs than unsecured loans like personal loans or credit cards.

• Length of Loan terms: Typically, shorter repayment timeframes can result in lower APRs than longer terms. However, shorter terms also typically result in higher monthly payments so it’s important for borrowers to understand their monthly payment commitments.

• Market rates: Benchmark rates determined by market conditions can cause APRs to fluctuate for things like credit cards and variable-rate loans.

• Down payments: Providing a larger down payment on certain loans like mortgages or auto loans can reduce the loan-to-value ratio and potentially result in a lower APR.

How to qualify for lower APRs

• Focus on improving your credit score: You can help lower your credit score by paying bills on time, keeping credit utilization below 30%, and not opening too many new accounts.

• Decrease your debt-to-income (DTI) ratio: By paying down existing debts, you can make it more likely that you can qualify for better rates.

• Transfer balances to lower interest cards: Many new credit cards may offer an introductory APR of 0% for the first year or so. By moving higher-interest debt to one of these, you can help to improve your DTI ratio and pay off debt faster. But, make sure you pay attention to any transfer fees, which can range between 3% to 5%.

• Try negotiating with your lender: If you have a strong history of on-time payments, a long-standing relationship, or have improved your credit score, you may be able to negotiate a better rate with your lender or card issuer.

How lenders calculate APR in practice

Calculating APRs is just as complex for lenders as it is for borrowers. And, accuracy is critically important to ensure compliant, fair lending practices and accurate accounting.

Every lending business needs to make sure they have performed the correct calculations to feed into the loan contract and inform the customer how their loan will be serviced. Centralized core lending software allows lenders to eliminate manual loan calculations and ensure calculations are complete, accurate, and compliant with TILA regulations.

With manual APR calculation methods, some of the most common issues occur when businesses don’t include daily interest accrual, forget certain fees, don’t account for irregular payment periods, or simply round to the wrong decimal (Note: OCC requirements call for 4 decimal places to ensure accuracy).

But, the right loan management system can automate these APR calculations and safeguard against costly compliance mistakes with built-in tools that take into account standards from the Office of the Comptroller of the Currency (OCC) and Truth in Lending Act (TILA).

For example, LoanPro’s API calculator allows lenders to create API requests to pull in loan configuration settings to calculate everything from APRs to amortization schedules to daily interest accruals. This configurable, API-first approach allows lenders to deliver near-instant loan offers within their own application to prospective borrowers, without needing to create a new loan in the system.

Understanding loan calculations can become complicated for borrowers and implementation for lenders relies on accuracy and consistency. Bottom line: APR is the most accurate way for borrowers to compare loan costs. And, automating those calculations can ensure accuracy and compliance for lenders.

Automate APR calculations with LoanPro's API calculator

Try LoanPro’s API calculator today to take advantage of benefits like:

• Automated, built-in compliance for APR calculations and TILA/Reg Z requirements
• Real-time calculations for APR, TILA disclosure numbers, payment amounts, simple payment schedules, and full amortization schedules
• Flexible options to leverage as a standalone API or part of LoanPro’s loan management system

APR calculation FAQ

What's the difference between APR and interest rate? While both are shown as a percentage, there is a big difference between APR and interest rate. Interest rate is the base percentage charged on the principal amount borrowed. APR includes the interest rate plus any lender fees, insurance, and closing costs.

How is APR calculated on a loan? APR is calculated using the following formula: APR = ((Interest + Fees / Loan Amount) / Number of Days in Loan Term) × 365 × 100

Does APR include all loan fees? APR includes any initial fees associated with a loan, such as closing costs, origination fees, and more. However, it does not include every fee that may be incurred. These can include late payment fees, property taxes, insurance (car or home), or third-party services.

Can APR change after I take out a loan? Some loans or credit cards may have a variable APR that can fluctuate over time based on market benchmarks.

Why is APR higher than my interest rate? APR is typically higher than an interest rate because it includes additional fees associated with a loan that aren’t included as part of the interest rate.

How do lenders ensure accurate APR calculations? The best way to ensure accurate APR calculations as a lender is to automate them with the right loan management system.

What is APR vs APY? An APR is the total cost of borrowing money, including fees and interest rates. An Annual Percentage Yield (APY) is the amount you earn on savings based on compound interest. Put even more simply, APR is costs while APY is earnings.