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### Course: Finance and capital markets>Unit 1

Lesson 3: Credit cards and loans

# Annual percentage rate (APR) and effective APR

APR stands for Annual Percentage Rate. It's the yearly interest rate you pay on a loan or credit card. However, a credit card's advertised APR isn't the true interest rate because it compounds daily. Learn how to calculate the effective APR to find a card's true interest rate. Created by Sal Khan.

## Want to join the conversation?

• sal compounds the multiplier (which is 1.006274) by 365 times in a year. But shouldnt he compound the multiplier by 364 times/ year instead? I think this because he says that he receives his money on day 1, and on day one, he doesnt multiply the money by anything because he just received the money on that day. And so, if he doesnt compound the money on the first day, there are only 364 days left in the year, so why doesnt he compound the money by 364 times instead??
• Good catch. Technically yes, if you include day one (where no interest was charged), then at the end of 365 days, only 364 days of compounding would have taken place. Sal's goal was to calculate a year of compounding, so that's why he raised 1.0006274 to the 365th power (which means that the 365 days start after day one). But you're right: if you count day one as the day you put the money on the card like he did, the number should be raised to the 364th power.
• In the last step, how come it goes from 1.257 to 25.7%. Shouldn't it be 125.7%? What happens with the 1, can someone explain to me? Thanks
• The 1 represents the original amount of money over which you pay the interest. So its 100% of capital and 25.7% of iterest, 125.7% total.
• What is the difference between APR and APY?
• APR is the rate of interest you are being paid. APY is the actual return you are getting once you factor in compounding.

For example, suppose you have two different investment vehicles, and they both pay 4% interest (APR). However, one compounds daily and the other one monthly. The APY will be higher for the vehicle that compounds daily.
• Why does he say he would 1.257 times his original principal amount, and then he says his effective interest rate would be 25.7%? Wouldn't it be 125.7%? I don't understand where he got that 25.7% from. If he was using that initial 1.257, if you change that into a percentage, it wouldn't be 25.7%, would it?
• Jacob, great question!. You are correct that 1.257 = 125.7%, but here we are just trying to find the interest or the amount added to the principal. So we just look at the amount above 100%, which is the 25.7%. So in these types of problems, we find some result (which is 1 + interest rate) and then subtract the 1 to isolate the interest rate.
APR - is something wierd.

Hope I get an idea of compound interests, so, it's all about applying some interest from cycle to cycle, but why do we have compound interest's interpritation here?
If somebody state to me, that my annual percentage rate is 22.9% and it all dividing into parts by day,
a will think that in looks something like dividing percents by 365 parts and then applying to my initial credit, likewise our credit is 1000, so bank got it and take 22,9 percent out, then divide into 365 days and charge off day by day. It's even sounds so, APR, the first word here - ANNUAL, hence if I got 1000, to the next year I'll must pay off 229\$ that exactly 22.9% from my initial loan. I can't understand how they can apply compound interests when somebody states about 22.9% per year, or, to state 22.9% per year when has compound interests and some rate per day that eventually doesn't equal to annual...
• Great question Mark. I think you are asking "why do they have a simple interest calculation like APR represent compound interest? Why not just use effective APR?"

I have thought about this quite a bit and I am wondering the same thing. I can only note that there are different types of APRs and many different types of loans, so an APR must be an effective tool in certain situations.
• I do not understand how Sal went from 0.6724% to a decimal of 0.0006724. Could someone please explain how he got the latter?
• Sami, he got the 0.06724% by dividing the 22.9% by 365, the number 0.06724% is how much the bank compounds the principal daily. Now that you have the 0.06724%, Sal then turns this number into a decimal by moving the decimal point over two places to the left, thus giving you the latter of 0.0006724 (which is the decimal notation of 0.06724%).
• at 3,22 why does Sal adds 1 to 000,6274?
• It is the principle + 1 period of interest.
• So I appreciate this video! I thought they compounded monthly not daily so I assumed I was not paying interest on the 30 days after I make a purchase. I checked my credit card information and found that there is no charge to the first 25 days after the after the billing cycle and YTD I have paid \$0.00. So I am glad that I am not automatically paying interest. However, do most companies offer a grace period?
• The grace period only applies if you paid your bill in full the prior month, and if you take no cash advances.
• So after you find the effective interest rate, do you just multiply it to the principle to get the true final cost?
• apr is annual percentage rate. If you barrow money from a credit card company you will end up spending more money paying them back then you borrowed from them.
• I was always under the assumption that if you pay your credit card off monthly, you will never be charged interest. If the interest is compounded daily, do they charge you the daily interest on the balance held at the end of each day? Meaning should I be paying off my credit card daily? Or do they compound the daily balance and only charge it if it's not paid off at the end of the month?
• @Andrew, you are right! However, theoretically, you'll end up paying less if you pay interests daily that paying it monthly because, there will be new interest calculated for the interest that was unpaid for the 30days! Hope it makes sense!