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This article was co-written by Hannah Cpe. Hannah Cpe is a tax advisor and founder of Sunlight Tax. As an artist and tax professional with over 10 years of experience in the freelance tax field, Hannah specializes in tax treatment for independent creatives and small businesses, helping creative individuals build their businesses. entrepreneurship, and personal finance support in the creative sector. She holds a tax advisor license, which is a certification of tax expertise and representation from the IRS. She has been invited by organizations such as Harvard Ed Portal, Boston Foundation, New York Foundation for the Arts, RISD and Cornell University to give tax presentations to artists. Hannah holds a bachelor’s degree in Art History from Yale University, a master’s degree in Drawing from Boston University, and studied accounting at Brooklyn College.

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When considering a loan or investment, it can be difficult to visualize the actual cost of the loan or the actual return on the investment. There are many different terms used to describe the interest rate or profit on a loan, including annual percentage rate, effective interest rate, nominal interest rate, etc. Of these, the effective interest rate is probably the most useful because it gives you a relatively comprehensive view of the true cost of the loan. To calculate the effective interest rate on a loan, you need to know the loan terms and do a simple calculation.

## Steps

### Get the necessary information

**Familiarize yourself with the concept of effective interest rates.**Effective interest rate is used to describe the total cost of a loan; it includes the effect of compounding which the nominal or “published” rate does not take into account.

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- For example, a loan with a compound interest rate of 10% a month actually has a 10% higher interest rate because interest is compounded monthly.
- Effective interest rates do not include one-time fees, such as loan initiation fees. These fees are charged in annual percentage interest.

**Determine the published interest rate.**The published interest rate (also known as the nominal interest rate) is expressed as a percentage.

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- The published interest rate is usually the “advertised” interest rate. That’s the number that lenders usually give to announce their interest rate.

**Determine the number of interest compounding periods for the loan.**The compounding period is usually calculated on a monthly, quarterly, yearly or continuous basis. This number represents the number of times interest is compounded.

^{[3] X Research resources mathforum.org/dr.math/faq/faq.interest.html}

- Usually the compounding period is calculated on a monthly basis. However, you should still check with your lender to be sure.

### Calculate effective interest rate

**Familiarize yourself with the formula for converting published interest rates to effective interest rates.**The effective interest rate is calculated using a simple formula: r = (1 + i/n)^n – 1.

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- In this formula, r represents the effective interest rate, i represents the published interest rate, and n is the number of compounding periods per year.

**Calculate the effective interest rate using the above formula.**Take, for example, a loan with a published interest rate of 5% and compounded monthly. Using the above formula, we have: r = (1 + 0.05/12)^12 – 1, ie r = 5.12%. The same loan, but the compounding period is calculated in days, we have: r = (1 + 0.05/365)^365 – 1, ie r = 5.13%. Note that the effective interest rate will always be higher than the published rate.

**Familiarize yourself with the formula used in the case of continuous compound interest.**If interest is compounded continuously, you need to calculate the effective interest rate using another formula: r = e^i – 1. In this formula, r is the effective interest rate, i is the published interest rate and e is the constant 2.718.

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**Calculate the effective interest rate in case of continuous compounding.**Take, for example, a loan with a nominal interest rate of 9% with continuous compounding. According to the above formula, we have: r = 2.718^0.09 – 1, ie 9.417%.

**After reading and understanding the theory, you can simplify the calculation by the following.**

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- After getting familiar with the theory, you can solve the calculation in another way.
- Find the number of periods in a year. The number of periods in the year will be 2 for semiannual, 4 for quarterly, 12 for monthly and 365 for daily.
- Number of periods per year x 100 plus interest. If the interest rate is 5%, it will be 205 for semiannual, 405 for quarterly, 1205 for monthly, 36505 for daily.
- Effective interest will be the value of the excess of 100, in the case of a capital of 100.
- Do the following calculation:
- ((205÷200)^2)×100 = 105.0625
- ((405÷400)^4)×100 = 105,095
- ((1205÷1200)^12)×100=105,116
- ((36505÷36500)^365)×100 = 105.127

- The excess of 100 in case ‘a’ is the effective interest rate compounded semiannually. Thus, 5.0625 is the effective interest rate for the semiannual period; 5,095 for quarterly; 5,116 for monthly, and 5,127 for daily.
- You just need to memorize in theorem form.
- (Number of periods x 100 plus interest) divided by (number of periods x 100) to the power of periods, the result is multiplied by 100. Anything over 100 will be the effective interest rate.

## Advice

- There are many online calculators that you can use to quickly calculate effective interest rates. In addition, the EFFECT() feature in Microsoft Excel will help you calculate the effective interest rate knowing the nominal interest rate and the number of compounding periods.

## Things you need

- Pencil
- Paper
- Computer

This article was co-written by Hannah Cpe. Hannah Cpe is a tax advisor and founder of Sunlight Tax. As an artist and tax professional with over 10 years of experience in the freelance tax field, Hannah specializes in tax treatment for independent creatives and small businesses, helping creative individuals build their businesses. entrepreneurship, and personal finance support in the creative sector. She holds a tax advisor license, which is a certification of tax expertise and representation from the IRS. She has been invited by organizations such as Harvard Ed Portal, Boston Foundation, New York Foundation for the Arts, RISD and Cornell University to give tax presentations to artists. Hannah holds a bachelor’s degree in Art History from Yale University, a master’s degree in Drawing from Boston University, and studied accounting at Brooklyn College.

This article has been viewed 39,488 times.

When considering a loan or investment, it can be difficult to visualize the actual cost of the loan or the actual return on the investment. There are many different terms used to describe the interest rate or profit on a loan, including annual percentage rate, effective interest rate, nominal interest rate, etc. Of these, the effective interest rate is probably the most useful because it gives you a relatively comprehensive view of the true cost of the loan. To calculate the effective interest rate on a loan, you need to know the loan terms and do a simple calculation.

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