APR Calculator

The APR calculator shows the actual annual cost of a loan taking into account fees and not just the nominal interest rate. By entering information for a conventional installment loan or mortgage, including fees and points, it will show the annual percentage rate, monthly payment, and total cost of the loan over its entire term.

What is the APR?

APR stands for Annual Percentage Rate and is an indicator of cost that takes into account all the costs over a year and includes the nominal interest rate as well as fees and other charges levied by the lender on the loan. Because it takes both interest and fees into account, APR provides a fairer basis for comparing different credit products.

Customers often confuse the APR with the interest rate. The interest rate is just the cost of borrowing money and doesn't include any processing fees, points or closing costs. Even if two loans offer the same interest rate, the actual cost can vary significantly when those fees are factored in, and the APR makes that difference clear.

In the United States, lenders are required by law to disclose the APR under the Truth in Lending Act so that borrowers can compare credit costs on an equal basis. Because each lender aggregates fees differently, it is best to obtain a detailed breakdown of the costs included in the APR from the provider.

The difference between APR and interest rate.

You can think of the interest rate as the price of capital and the APR as the total cost of a transaction. If there are no fees associated with a loan, then the APR will be equal to the interest rate. However, if there are processing fees, discount points or closing costs added on, your APR will be higher than the interest rate because you're paying more for the same amount of money.

This calculator illustrates the difference. If you enter an interest rate with no fees, then the APR is equal to the interest rate. Notice how the APR increases when you add a fee. On the other hand, your monthly payment can stay the same because it depends on both the interest rate and loan amount.

Calculation of the effective annual interest rate (APR)

The monthly rate is calculated with a standard formula for amortization loans. For a loan amount A the monthly interest rate i is the annual interest rate divided by twelve and repayment takes place in n months.

The effective annual interest rate (APR) is then the interest rate for which the present value of these repayments equals the actual amount received, that is, the loan amount minus any fees paid by you. We denote the monthly effective annual interest rate as j and the net loan amount as P.

Unlike the formula for monthly payment, this formula cannot be rearranged to solve directly for j. As there is no closed-form solution, the calculator uses the same method as a lender's computer would use to find an interest rate given the other variables.

A complete example:

Let's say you borrow $100,000 for 10 years at a rate of 6% and pay up front fees of $2,500. If you borrowed $100,000 at a rate of 6% for 120 months, your monthly payment would be about $1,110. However, you'd actually only receive $97,500 because the $2,500 is used to cover up front costs.

If we calculate the interest rate that would turn $97,500 into a cash flow with the same repayment of $1,110, then the effective annual rate (APR) is about 6.56%, which is higher than the stated interest rate of 6%. This difference of 0.56 points represents the cost in terms of an effective annual rate.

Use Mortgage Mode:

For a mortgage, switch to the Mortgage mode. Enter the property price and equity amount and the calculator will calculate the loan amount. The points are entered as a percentage of the loan amount with one point being equal to one percent. As points are treated as prepaid costs, they increase the effective annual rate (APR).

If the equity stake is less than 20%, add in annual private mortgage insurance (PMI). This calculator includes these costs monthly and stops calculating when the balance falls to 80% of the property value. These payments are added into the total cost and APR. Mortgage loans generally include origination fees, application fees, appraisal fees, processing fees, as well as mortgage insurance and discount points from U.S. lenders.

The annual percentage rate (APR) for a mortgage usually does not include certain costs such as appraisal fees, surveying costs, title insurance, home warranties and prepaid taxes and insurance. If you are unsure whether or not a particular fee should be included in the APR, ask your lender.

The difference between a fixed and variable APR:

A fixed APR stays the same throughout the life of your loan, which means that your monthly payments will also remain constant. A fixed APR is a safer option when interest rates are low and could potentially rise, though the initial rate will usually be slightly higher than with an adjustable rate.

A variable APR changes based on a reference index such as the prime rate and is then adjusted by an add-on from the lender based on your creditworthiness. It can start with lower rates, but it can also rise if the reference rates go up. The longer the term, the more potential impact these fluctuations have. This calculator uses a fixed interest rate so for a variable rate loan you should consider the result as the cost at the current rate.

The difference between APR and APY:

APR (Annual Percentage Rate) and APY (Annual Percentage Yield) sound similar but have opposite meanings. The APY is the effective annual interest rate, taking into account compound interest. Banks list the APY for savings accounts because compounding increases earnings. Loans are listed with APR because it's calculated without compounding so reflects a lower rate of return.

For the same nominal interest rate, the effective annual interest (APY) is always slightly higher than the annual percentage rate (APR). An APR of 10% that compounds monthly equates to an APY of about 10.47%. This calculator also shows the effective APR which applies the same compounding to the loan's APR and gives you a true annual figure.

APR limitations

The APR assumes that you keep the loan for its full term. If you plan to pay off your loan early by selling or refinancing it or making extra payments, then the actual impact of up-front fees is greater than what the APR indicates because those fees are spread over fewer years. When two loans have the same APR, people who plan to pay their loans off early will be better off with the one that has lower up-front fees.

The APR is also a comparative tool that can only be used for loans with the same currency and repayment terms. It does not give you any indication of whether or not you will be able to comfortably repay your loan, nor does it take into account the risks associated with variable interest rates. Don't look at the APR in isolation - check it along with your monthly payments and total cost, both of which are shown on this calculator.

This calculator is for general educational and planning purposes only, and does not constitute financial advice. Actual APRs, fees and terms may vary depending on the lender and borrower, and the APR quoted by a lender may have slightly different rules for how to treat fees. Always check an official offer before taking out a loan.