## Nominal and Periodic Interest Rates

Hello and welcome. In this video, we will talk about interest rates. There are 2 kinds of interest rates you need to know about.
Nominal rates and periodic rates. Let’s see what they are.
First, let’s look at the nominal interest rate.
The Nominal Interest Rate always has a certain compounding frequency.
It is written down as Jm, where m is the compounding frequency. The compounding frequency tells us how many times per year the rate is compounded.
For example, j2 – is the nominal interest rate compounded 2 times per year, it’s called nominal interest rate with semi-annual compounding;
This is the most common rate you will see in the course.
J12 is the nominal interest rate compounded 12 times per year, it’s called nominal interest rate with monthly compounding.
J365 – that’s nominal interest rate compounded 365 times per year, or nominal interest rate with daily compounding
Sometimes you may also encounter j4 – which is the nominal interest rate with quarterly compounding.
Another important rate that we will use in this course is j1.
This is the nominal interest with annual compounding, and it’s also called effective rate.
We will go over what this means exactly later, for now just remember that j1 is a special rate and it is also called the effective rate.
Now let’s talk about periodic interest rate.
What is periodic interest rate? The periodic interest rate is the rate per compounding period. Makes sense, right, periodic is rate PER PERIOD.
For example, if you have a nominal interest rate with semi-annual compounding j2 = 8%,
Your periodic interest rate is the rate per compounding period, so per half of the year.
So while the nominal interest rate is always the rate per year, the periodic rate is the rate per compounding period.
The periodic rate is written as i2 and it is simply half of j2, i2 = j2/2 = 4%.
So we have 2 compounding periods here and each period we add 4% to the loan.
Let’s look at another example.
What if we have a nominal interest rate with quarterly compounding j4 = 8%.
That means there are 4 compounding periods per year, and each period EACH QUAERTER we add 2% to the loan, because our periodic rate
I4 = j4/4 compounding periods = 2%.
So every compounding period we are adding 2% to the loan amount and we do it 4 times.
What if we have j12 = 12%.
That’s the nominal interest rate with monthly compounding.
That means that our periodic monthly interest rate is j12/12, 12%/12 is 1%.
So every month, we add 1% to the loan and we do it 12 times.
So you can see that nominal and periodic rates are connected.
If we know the nominal rate, we simply divide it by the number of compounding periods to get the periodic rate.
The general formula is im (the periodic rate) is equal to jm (the nominal rate) divided by m,
Where m is the number of compounding periods.
Like you saw in the examples, i2 = j2/2, i4 = j4/4, I 12 = j12/12 and so on.
You can also go the other way. If we know the periodic rate im, we can multiply it by the number of compounding periods m to get nominal rate jm.
So for example j4 = i4 x 4, j2 = i2 x 2, j12 = i12 x 12 and so on.
Let’s look at some examples of this reverse formula.
Let’s say you have the monthly periodic rate of 1 %. That’s your i12.
From it, you can find the nominal interest rate with monthly compounding, j12.
J12 is i12 multiplied by 12, so 1% x 12 = 12%.
If you have a quarterly periodic rate of 1.5%. I4 = 1.5%
And the question is asking you for nominal rate,
You can find the nominal rate with quarterly compounding by multiplying your periodic rate by the number of compounding periods,
J4 = i4 x 4 = 6%.
Ok, we have learnt how periodic interest rates and nominal rates are connected and how to get one of them if you know the other one.