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charge interest on these fees since they are attached to the loan amount.</p><p id="47ca">Fees paid separately — fees that are paid in advance or after the loan is completed. Interest is not charged on these fees, but it does increase the APR.</p><p id="b67a">If you find this post useful, you may find my post about rising mortgage rates valuable as well! <a href="https://readmedium.com/how-rising-mortgage-rates-affect-you-8ae174022f19">Check it out here!</a></p><div id="733f" class="link-block"> <a href="https://readmedium.com/how-rising-mortgage-rates-affect-you-8ae174022f19"> <div> <div> <h2>How Rising Mortgage Rates Affect You</h2> <div><h3>Prices of homes have soared due to low rates, but now the tables have turned.</h3></div> <div><p>medium.com</p></div> </div> <div> <div style="background-image: url(https://miro.readmedium.com/v2/resize:fit:320/0*7JJgD4LGaUthebzl)"></div> </div> </div> </a> </div><h1 id="60e8">How to Calculate APR</h1><p id="1fb6">Now that you understand how APR works and all the financial terms associated, let’s go over an example. We will assume that you are taking a mortgage of 200,000 and you will be paying it back monthly. A common mortgage will be for 30 years, and we will assume an interest rate of 6% that is compounded monthly. Additional fees will be 5,000 not including interest. The following steps can be used to calculate the EAPR:</p><p id="357c"><b>- Define the monthly payment</b></p><p id="1e95">This loan will compound monthly so we will divide 6% over 12 months to get 0.5% of interest per month.</p><p id="32ef">360 days will be used for a year.</p><p id="292f">The present value of the loan is 205,000 (loan amount + fees).</p><p id="556d">Payment = (205,000 * .005 * (1+.005) ^ 360) / (1+.005) ^ 360 = <b>1229.08</b></p><p id="3969">This tells us the monthly payment will be 1229.08.</p><p id="5aef"><b>- Estimate the APR</b></p><p id="000a">When calculating your loan payment, you will pay interest on additional fees plus the principal amount you receive. In this case, your payment amount should be compared to the original loan amount of 200,000 since this is what you received instead of 20,000 including fees.</p><p id="981b">To compute the periodic annual percentage rate (APR_i) we use this formula:</p><p id="1cec">1229.08 = (200,000 * APR_i * (1+APR_i) ^ 360 / ((1 + APR_i) ^ 360</p

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<p id="fd93">Solving this equation is complex and requires the use of the Newton-Rapson Method so we will not elaborate here. The APR_i calculates to be 0.519% in this example. Next, we just multiply this by the payment frequency of 12 giving us an estimated APR of 6.232%.</p><p id="9bab"><b>- Estimate the effective annual percentage rate</b></p><p id="8468">We know that the effective APR is the most accurate so let’s estimate it using the following formula:</p><p id="8b65">EAPR = (1 + .06232 / 12) ^ 12–1 = 6.413%</p><p id="720e">Therefore, when we include additional fees and compounding, our EAPR is 6.413% as opposed to just 6%.</p><h1 id="82fd">Before you go</h1><p id="7605">You can get all my stories sent directly to your inbox by <a href="https://medium.com/subscribe/@miketoneyhoffman">clicking here</a>!</p><p id="d79e">If you enjoy reading stories like these and want to support me as a writer, consider becoming <a href="https://medium.com/@miketoneyhoffman/membership">a Medium member</a>. The membership is $5 a month, giving you unlimited access to stories on Medium. If you <a href="https://medium.com/@miketoneyhoffman/membership">sign up using my link</a>, I’ll earn a small percentage.</p><div id="82bb" class="link-block"> 
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Banking | Finance | ILLUMINATION

Understanding APR: Don’t Let Banks Fool You!

Don’t let the banks use this trick on you.

Photo by Eduardo Soares on Unsplash

What is APR?

The annual percentage rate (APR) is an interest rate that refers to the amount of interest you will pay on a loan based on a percentage of the total loan amount. The APR is often used by financial institutions to inform customers how much they can expect to pay to take out a loan.

One of the key points to understand about APR is the fact that it does not include compounding. This is important because banks can make it seem like you are paying less than it may look. If you are quoted with an APR of 10% that is compounded more than once per year, then the total interest you will pay will be more than 10%. This is called the effective annual rate (EAR) when you take compounding into account.

The most common types of interest rates include the annual percentage rate (APR), effective annual rate (EAR), and effective annual percentage rate (EAPR). The most accurate one to use will be the EAPR because it includes compounding and any additional fees. The APR includes additional fees but excludes compounding. The EAR includes compounding but excludes additional fees. This means the EAPR includes everything making it the most accurate to use.

Using an APR Calculator

Now that you understand the important aspects of how APR works, you can learn how an APR calculator can make your life easier. To effectively use this tool, you must be able to input all the variables of your loan. You must know the following variables:

Loan amount — the amount you are borrowing.

Nominal interest rate — the interest rate excluding fees and compounding.

Loan term — the period in which you must pay off the loan.

Compounding frequency — how often the interest compounds.

Fees rolled into the loan — fees that are paid during the loan term — banks will generally charge interest on these fees since they are attached to the loan amount.

Fees paid separately — fees that are paid in advance or after the loan is completed. Interest is not charged on these fees, but it does increase the APR.

If you find this post useful, you may find my post about rising mortgage rates valuable as well! Check it out here!

How to Calculate APR

Now that you understand how APR works and all the financial terms associated, let’s go over an example. We will assume that you are taking a mortgage of $200,000 and you will be paying it back monthly. A common mortgage will be for 30 years, and we will assume an interest rate of 6% that is compounded monthly. Additional fees will be $5,000 not including interest. The following steps can be used to calculate the EAPR:

- Define the monthly payment

This loan will compound monthly so we will divide 6% over 12 months to get 0.5% of interest per month.

360 days will be used for a year.

The present value of the loan is $205,000 (loan amount + fees).

Payment = (205,000 * .005 * (1+.005) ^ 360) / (1+.005) ^ 360 = 1229.08

This tells us the monthly payment will be $1229.08.

- Estimate the APR

When calculating your loan payment, you will pay interest on additional fees plus the principal amount you receive. In this case, your payment amount should be compared to the original loan amount of $200,000 since this is what you received instead of $20,000 including fees.

To compute the periodic annual percentage rate (APR_i) we use this formula:

1229.08 = (200,000 * APR_i * (1+APR_i) ^ 360 / ((1 + APR_i) ^ 360

Solving this equation is complex and requires the use of the Newton-Rapson Method so we will not elaborate here. The APR_i calculates to be 0.519% in this example. Next, we just multiply this by the payment frequency of 12 giving us an estimated APR of 6.232%.

- Estimate the effective annual percentage rate

We know that the effective APR is the most accurate so let’s estimate it using the following formula:

EAPR = (1 + .06232 / 12) ^ 12–1 = 6.413%

Therefore, when we include additional fees and compounding, our EAPR is 6.413% as opposed to just 6%.

Before you go

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If you enjoy reading stories like these and want to support me as a writer, consider becoming a Medium member. The membership is $5 a month, giving you unlimited access to stories on Medium. If you sign up using my link, I’ll earn a small percentage.

Banking
Finance
Money
Business
Illumination
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