Amy has a master's degree in secondary education and has taught math at a public charter high school.
After watching this video lesson, you will understand how the interest rate that financial institutions, such as credit card companies, give you work. Also, learn how this interest rate may be different than the one you actually end up with.
Almost everyone has a credit card nowadays. There are lots of different credit card companies out there. They all want more customers, more people to carry their credit card. The way credit card companies work is that you spend money that you don't have, then you pay a small portion every month until you pay it off. However, each credit card has a stated interest rate that you also have to pay based on how much you owe. The credit card companies use this interest rate to calculate how much extra you have to pay each month. This interest rate is how credit card companies make their money. You will see the interest rate listed as an APR (Annual Percentage Rate). You will see such numbers as 10.99%, 23.99%, etc.
Effective Annual Rate
However, this number that you see is not the effective annual rate, the actual interest rate when the calculations are done more than once a year, because the interest rate that they show you is the interest rate if the calculation is done just once a year. With credit card companies, the calculations are done on a monthly basis. Let me show you the difference when the calculation is done once a year versus once a month.
Say we have an annual interest rate of 11%. If we have $500 in the account, then at the end of the year, we will have $555 if we make the calculation just once a year. Now, if we make the calculation on a monthly basis, at the end of the year we will have $557.86. We have slightly more here than when our calculation was done just once a year.
This tells us that if we calculate the interest more than once a year, then we need to adjust our effective annual rate to account for this.
The good news is that we already have a formula in place to do just that.
In this formula, the i stands for the interest rate that is given to you by the company. The n is the number of times that calculations are made in a year. So, if calculations are done on a monthly basis, the n is 12. When using this formula, we change our percentage to decimal form.
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Let's use this formula for our 11% annual interest rate and see what our effective annual rate is when our calculations are done on a monthly basis. Plugging in 0.11 for i and 12 for n, we have (1 + 0.11 / 12)^12 - 1 = 0.1157 for a percentage of 11.57. So, our effective annual rate is 11.57%.
Is this correct? If we make just one calculation using this effective annual rate on our $500 balance, at the end of year, we will have $557.85. We are 1 penny off because we have rounded our effective annual rate to just two decimal places. So, our effective annual rate is correct.
See if you can do this problem on your own:
Calculate the effective annual rate for an interest rate of 15% when the calculations are done on a monthly basis.
Our interest rate is 15, so our i is 15. Our n is 12 since the calculations are done on a monthly basis. So, plugging in this information into our formula, we have (1 + 0.15 / 12)^12 - 1 = 0.16075. So, our effective annual rate is 16.07%. Is this what you got?
Let's review what we've learned now. The effective annual rate is the actual interest rate when the calculations are done more than once a year. The formula for the effective annual rate is:
The little i stands for the interest rate that is given to you and the n is the number of times a year that calculations are made. Using this formula will give you the effective annual rate if the calculations are done more than once a year. Most often the n is 12 for monthly calculations.
Measure your ability to do the following after watching this video lesson:
Provide specifics about the effective annual rate
Distinguish between the effective annual rate and the annual percentage rate
Illustrate the formula for calculating the effective annual rate
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