 # Effective Interest Rate vs Nominal Interest Rate | (EAR vs APR) | Explained with Examples

##### In this lesson, we explain what Nominal Interest Rate (APR) and Effective Interest Rate (EAR) are. We explain and show the formula of how to calculate the effective interest rate. We also explain and go through examples of the difference between the effective interest rate (EAR) and nominal interest rate (APR). We explain the effect of compounding thoroughly here. Check it out.

Welcome to contacts this lesson we are going to be looking at effective interest rates or ei r versus nominal interest rate or apr otherwise known as annual percentage rate what are these rates here nominal interest rate is a rate that does not take compounding into account so it’s a simple interest rate in other words it is also known as the stated interest rate

It is stated as a simple interest so nominal interest rate is simple interest rates where it does not take into account compounding and you’ll understand much more just not effective interest rate is a rate that takes compounding into account it is the actual annual rate considering the compound compounding so you take compounding into account for you to know what

Is the actual rate that i am paying considering that these compounding effects over they if there is compounding the effective interest rate is higher than the nominal interest rate that’s always the case if you have more than one compounding during a period then effective interest rate is higher than the nominal interest rate if the interest rate is compounded once

Per he per annum or per year the rates would be the same so if the controlling you do it once per year then the rates would be the same for both the effective interest rate and nominal interest rate but otherwise if there is compounding during the period more than one compounding then you will see that the effective interest rate is always higher than the nominal

Interest rate so let’s get much more into it for you to understand what we mean here is the difference between the nominal interest rate and they effective interest rate here’s an example a bank charges 12 percent per annum compounded monthly on a loan of 2,000 rain so a bank try just first of 12 percent per annum and we are told here that it’s compounded monthly so

Obviously that is 12 12 periods that is being compounded so it’s not compounded once so it’s 12 percent per annum compounded monthly on a loan of 2,000 ren what is the nominal interest rate the nominal interest rate is the spacer interest rate which is we are told here is 12% so that is the nominal interest rate simple interest rate now we know here that there is

Compounding and it’s compounded monthly so we know that that 12% it’s pay our number it’s compounded monthly the nominal interest rate that is stated here is what the bank would also stay but we know that if it’s compounded monthly then we are paying interest on interest and that is what compounding means so you will need to calculate or the effective interest rates

To get the equivalent interest rate that you will actually be paying on this loan so let’s take a look at this the compounding is monthly so it’s 12% divided by 12 months to get one percent per month that means every month we are paying 1% on the loan itself and remember we are not just paying 1% on the lawn we’re playing one person on the loan plus the interest

Each month and let me explain how that works for the nominal interest rate we have 12% times 200 ran we get 24 and simple interest that is what the nominal interest rate is trying to tell us that for nia if it was simple interest would be paying 24 and for one year but we know here that there is compounding effect here that is why the nominal interest rate is not

The best rate oh it’s not the most accurate rate to tell us how much we actually pay as a percentage but because of compounding we know that we are paying actually one percent a month so if they are paying 1% a month how much is the effective interest rate and that is what we’re trying to calculate and there is the main difference between nominal interest rate and

Effective interest rate so if we are paying 1% per month the interest in the first month will be 12% divided by 12 months times 2,000 grand that means in the first month we will have paid or will have incurred an interest of 20 right well then what about in the second month how much interest we have incurred well we didn’t care the interest of 12% divided by the

Twelve months times 2,000 plus the 20 right now do you see here that it’s interest on interest we incurred 20 grand in the first month as interest and in the second month we incurred 20 grand 20 cents so 20 point to rent and how did we get that we took the 2,000 ran the initial loan amount class the interest didn’t cut in the first month to get the interest for

The second month so you can see here that it’s piling up we are paying interest on the money that you borrowed on the loan of 2010 plus we are paying in we are also paying interest on the interest that we have incurred as well from the first month that is what compounding means now the question is what is the annual rate considering that we are paying interest on

Interest what is the actual interest that we are paying back to the bank well there is what is called the effective interest rate the nominal rate the mahna mahna interest rate of 12% is simple interest it does not take compounding into account but you know that you are paying interest on interest as we have seen down here the question is how many percent who will

Repay in a full year and here is the formula and an example on out carefully the effective interest rate the formula for the effective interest rate or the ei r is 1 plus r and by are you mean the interest day the interest the nominal interest rate or the interest rate that you are given divided by the number of compounding in the period and that answer to the

Power of the number of compounding in the period so you can see m here we are talking about the number of compounding so it’s 1 plus the interest rate divided by the number of common compounding in the period and we and that we take that ^ number of compounding in the period as well and then we take that answer minus 1 to get the answer now that may seem too much

But you will understand now let’s take it with it at this example a bank charges 12 percent per annum compounded monthly on a loan of 2010 so it’s compounded monthly on the loan of 2010 now already we know that is 12 as this chart i said that is quoted here is the nominal interest rate it does not take it has not taken the compounding into account so we know that

We need to calculate our effective interest rate and our effective interest rate we have the formula is 1 plus the rate which is 12% and we divide that by the number of compounding in the period which we are told here is compounded monthly so it’s divided by 12 it’s compounded monthly so it’s 12 months and then that answer to the power of 12 months as well because

That’s the number of compounding and then once we get that full answer we minus 1 to get the answer obviously can multiply by hunger to get it in percentage form but let’s look at it it’s 1 plus day interest rate which is 12 percent or 0.1 2 divided by the number of compounding in just 12 months because compounded monthly and that’s ^ 12 months because that’s then

Compounding period and then we minus 1 and then we get an answer of twelve point six eight percent you’ll get zero point one two six eight multiplied by hundred to get to that twelve point six eight percent that is the effective interest rate so in in real terms you’re actually paying an interest of twelve point six eight percent back to the bank considering that

There’s compounding in clays here so there is the rate that you want to be looking for to see how much might be in one year considering that i’m paying interest on interest on this loan it’s twelve point six eight percent that is the effective interest rate let’s look at another example quickly over here we are told that a fixed deposit and seven percent per annum

Compounded quarterly what is the effective interest rate so here we’re a fixed deposit which burns seven percent per annum compounded quarterly what is the effective interest rate now what i want you to do here is to pause and try and calculate the effective interest rate using the formula that i’ve given you a path here and see if you’ll get the same answer that

Will get it here so you can pause and try and do it okay i hope that you’ve done it and you’ve gotten the answer so let’s look at this question we are told it’s seven percent so it’s one plus the rate which is seven percent so it’s one plus seven percent or zero point zero seven so you just take seven percent right behind red to yet seven divided by hundred to get

To zero point zero seven and then you divide that by the number of compounding in the period how many components do you have it’s 8c it’s compounded quarterly well we know that there are four quarters in the year so it’s four that’s the number of component in the period and that to the power of four was the number of compounding and – that answer by one and then

We’ll get our effective interest rate so let’s see what it is here one plus zero point zero seven divided by 4 to the power of four and then minus that by one and then we get a rate of seven point one nine percent now there is our effective interest rate now you notice here i remember i’d mentioned at the beginning that the effective interest rate will always be

Higher than the nominal interest rate or the stated interest rate because effective interest rate takes compounding into account so you can see here our nominal interest rate is 12% but our effective interest rate is twelve point six eight percent so it’s higher and here our nominal interest rate is 7% and i effective interest rate is seven point one nine percent

So you can see how effective is always higher because of the number of compounding but if it’s compounded once they will all be the same now that we’ve explained what the effective interest rate is what the nominal interest rate here is i want you to see a comparison between the two here on my left hand side i have nominal interest rate and here in black i have the

Effective interest rate where it’s compounded it takes compounding in into account i found this a similar table online and i thought this would be very helpful for you to see the difference if it’s compounded monthly you can see what the effective interest rate will be for 5% compounded monthly it’s five point one two percent if it’s compounded quarterly it’s five

Point zero nine percent if it’s compounded semi-annually sorry i don’t write that you can’t see the other words but it’s semi-annually it’s five point zero six percent but if it’s compounded annually look at this in nominal interest rate you can see is five percent compounded monthly quarterly semi-annually that different effective interest rate is higher but

If it’s compounded annually with compounded ones that is you can see that effective interest rate is the same as the nominal interest rate now that is what i meant at the beginning so if you try and plug in the formula that i gave you yeah elya you can try and plug it in and see what the compounding is monthly you’ll be able to get these answers over here it’s

Compounded quarterly with compounded semi-annually you should be able to get the answer so you can see the effective interest rate takes into account a compounding and it’s higher than the nominal interest rate so again when you’re looking at interest rate with the bank or with an institution or you want to invest somewhere if it takes into account compounding or

Its interest on interest try and get what the effective interest rate is to get the real rate that it’s costing you or that you are earning hope this has made sense we have done or another lessons where we show you how to calculate the effective interest rate and how to work backwards to get there the nominal interest rates using the financial calculator if you’d

Like to check that lesson out you’ll find a link in the description below otherwise if you’ve came to value from this lesson if you’ve learned something new is consider subscribing to our channel like this video and share it to those you think it might help till next time just