Hello everyone, welcome back to a new video.
Today's video will be our second video on Simple Interest.
In the first video, we saw the difference between Simple
Interest and Compound Interest.
So, let's move ahead to the formulas of Simple Interest and
see what type of questions are asked on it.
In the next video, we will do the same for Compound
Interest.
So, Simple Interest is comparatively easier than Compound
Interest.
In the last example, we saw that every year the interest
will be the same.
For example, Rs.1000 will be the same every year.
Because we use the same principal value which we have put
from the beginning.
So, let us suppose that the first term which we should know
is the principal value.
What is the principal value?
The principal value is the money which you are giving to
someone or depositing it somewhere.
So, the principal value is the money which you are
investing from the main money.
Then, you are asked what rate of interest you are giving.
The rate of interest comes next.
Now, what is the rate of interest? The rate of interest is
calculated per annum.
It is calculated according to the year.
It is calculated according to the half year.
It is calculated according to the quarter.
It will be different.
But, the main thing which we will take is the rate of
interest which is calculated per annum.
The rate of interest will be in percentage.
So, let us suppose that the rate of interest is in
percentage.
Let us take the principal value as P.
And then, we will have a time period.
We are talking about the time period for which we have lent
money or deposited money.
So, the time period comes next.
Let us denote it with T.
Then, we have the simple interest.
What is the simple interest?
Simple Interest or you can write it as SI.
The formula for SI is PRT divided by 100.
Multiply these three things.
That will be our simple interest.
Now, you will say that you are multiplying but there is 100
in the divide.
In that divide, whose 100 is there?
We have studied in the chapter on percentage.
If we want to change anything in percentage into fraction,
then we have to subtract the sign of percentage and divide
it by 100.
So, we have done the same thing here.
We have done R by 100.
So that it comes in fraction.
So, instead of 8%, we have done R by 100.
If you want to change this 8% in any other terms other than
percentage,
then you can directly write PRT.
In that you will not need to divide by 100.
When will we need to divide by 100?
When the rate of interest is given in 8%.
This rate of interest is per annum.
This is the time period.
This is our principle.
The sum of money we have deposited or invested in someone
at the start.
Then, this interest is extra money.
We are getting interest from above in this deposited money.
Or the land we have invested in.
So, one term comes here.
Amount or final sum.
This is also called as sum.
The amount you will get in the final amount.
After taking all this interest, after so much time period,
How much total money you will get?
So, you will get your deposited amount.
If you have not taken it out, then you will get this
principle.
Plus, if you take interest on it, then you will get add-on
interest.
So, this principle plus simple interest, we get the amount.
So, in principle, you add interest, simple interest.
You will get the desired or required amount.
So, if we add simple interest, first of all, we will find
out the amount.
We will find out simple interest with the help of this
formula.
And, we will add principle value in it.
So, we will get the amount.
So, this is the main formula of simple interest.
PRT by 100.
And, this is the formula for your amount.
Now, what is the relation in this?
As you can see this formula.
SI is equal to PRT upon 100.
So, in front of SI, you can see directly proportional.
In front of SI, from P, from principle value,
The more your principle value increases, the more your SI
will increase.
As your rate of interest increases, the more your SI will
increase.
If for longer duration, if you have deposited money for
longer duration, then your time period increased.
So, directly what happened to it?
Your SI also increased.
So, what we get from this formula?
This SI is directly proportional to principle.
It is directly proportional to rate of interest.
And, it is directly proportional to time as well.
What is the relation of these three?
It is directly proportional.
If you are told that in some time period, your principle
amount is doubling.
So, as before, we have a principle amount.
In that, we are getting interest, SI.
Now, if our R and T are same, then our principle amount
will be doubled.
And, R and T are same.
So, now what will happen?
What will be the relation of value of SI with previous SI?
What will be the relation between this SI and previous SI?
Earlier, our principle amount was P.
Now, it is doubled.
So, it will be multiplied by 2.
Now, what will be the relation between P and SI? 2P into R
T divided by 100.
So, what will be the relation between SI and P?
Now, this new SI will be 2P R T upon 100.
Now, this value will be equal to our old SI.
So, what will be the relation between SI and new SI?
It will be equal to twice of old SI.
So, if our principle amount is doubled, then our simple
interest will also be doubled.
Similarly, if there is any change in R, let us suppose, R
is multiplied by 5, then our old SI will also be multiplied
by 5.
So, these three are directly proportional.
Next, we will see that, if we are given a particular year,
like every year, our rate of interest is different.
If you give money to someone, you tell him that if you pay
this money within a year, then I will give you only 2% rate
of interest.
But, if you do not do this within a year, then I will
increase your next year rate of interest for the next two
years.
I will increase your rate of interest for the next two
years by 3%.
Then, if you are not able to pay, then I will increase your
rate of interest by 5%.
So, for different time periods, we are getting different
rates of interest.
As time goes on, what will be the relation between SI and
new SI?
SI would be, like for the first year, for what time period
is this?
This is our R1 rate of interest for the time period T1.
R1 is in per annum.
Suppose, this is our R2 rate of interest for the time
period T2.
Similarly, this is our R3 rate of interest for the time
period T3.
So, what will happen?
We have to solve these individually.
For example, if the principal amount is same for everyone,
then we will solve the case of T1 and R1.
So, for the first time, what will happen?
P R1 T1 divided by 100.
This will be done.
Now, we have to add for the future.
Today, we will add only.
So, we will do plus.
Then, the principal value is same as P.
So, we will do R1.
Now, our rate of interest has increased.
R2.
And, we will enter the time period.
Divided by 100.
Similarly, we will do the same for the third case.
R3.
T3.
By 100.
Now, what is common in these? Common is P by 100.
Or, you can take only P. No problem.
So, this is R1, T1.
Plus R2, T2.
Plus R3.
T3.
What will happen?
We will have this.
Simple interest.
When we have different rate of interest for different time
periods.
If the rate of interest is changing every year.
Then, what will happen?
This formula will be formed.
There is no need to remember this formula.
Basically, you should know the concept.
That we have to do PRT by 100 of simple interest.
Now, when there are different interest.
Then, at different times, different SI will come.
So, what to do with all of them?
Add them.
Then, we will get the total interest.
Nothing else in that.
So, this is your simple interest for different rate of
interest for different time periods.
Okay.
Now, suppose you have to convert the rate of interest.
The rate of interest will be given per annum.
But, let us suppose it is given per annum.
What is the rate of interest?
Let us suppose, the rate of interest is 10% half yearly.
Means, if the rate of interest for half a year is 10%.
Then, if you have to convert the rate of interest for the
whole year.
Then, what will happen?
If the rate of interest is 10% for 6 months.
Then, the rate of interest for the remaining 6 months is
also 10%.
And, how will the total rate of interest be formed? 6 plus
6 months.
1 year divided by 12 months.
Then, what will happen?
We will give 10% first.
Plus 10% for the remaining 2 years.
So, what will be the total rate of interest?
If we convert it per annum.
Per annum.
Then, it will be 20% per annum.
So, what we mostly try to do is.
That, our rate of interest should remain in per annum.
Is it clear to everyone?
That, what all we have done till now?
Next, if we see a question.
Let us see the question.
What does your question say?
Question says.
What is your particular thing?
You have deposited money somewhere.
And, you are depositing Rs. 80,000.
What are you doing?
Deposit.
What is the rate of interest?
Your rate of interest is 16.2 by 3% per annum.
And, for how many months are you doing all this?
You are doing all this for 9 months.
So, you tell me.
What will be your SI, Simple Interest?
Okay? First of all, you have to see.
What all are given to you?
What is given in this?
See, if you are depositing Rs. 80,000.
Then, what is this?
Is this your principal value or amount?
You are depositing.
From where I said deposit.
What will that be?
That will be your principal value.
That is Rs. 80,000.
Then, your R percentage.
That is rate of interest.
16.2 by 3% per annum.
So, what is the rate of interest? 16.2 by 3%.
Now, what is the time period given to you?
Time is given to you.
9 months.
Note one thing.
As I told you.
What is the R percentage we take?
Either we take per annum.
Similarly, what was T?
It was in years.
Time period in years.
So, here we have 9 months.
So, first of all, we will convert it into years.
What do we need?
We need time in years.
So, if we want to convert 9 months into years.
So, what will we do?
Divide by 12.
Because 1, 12 months are in 1 year.
12 months are in 1 year.
So, 9 will be 9 divided by 12 years.
If you want to convert a month into years.
So, you will divide by 12.
If you are given days.
So, you will divide by days.
Total number of days in a year.
That is roughly Rs. 365.
So, divide by 365.
So, you will get.
Conversion of days into years.
So, here we have 9 by 12 years.
That is, cancel out from 3.
If this happens.
So, 3 x 3 is 3 x 4 years.
So, you have P.
You have R.
You also have T.
So, you will get S.I.
S.I. would be.
PRT upon 100.
PRT divided by 100.
That would be Rs. 80,000.
Into 16 x 2 x 3.
16 x 2 x 3.
Into.
How much is the time? 3 x 4.
Divided by 100.
0, 00, 00 cancel.
In this fraction, change it improperly.
This is 800.
Into.
Divide by 3.
Bring it down.
And 4 also.
Bring it down.
Then what will happen?
If we do this.
16 x 3.
16 x.
This is 16 x 3.
That is 18.
1 x 3 x 3.
48.
48 plus 2.
That is 50.
So, this is 50.
Into this 3.
3 x 3 cancel.
4 x 1.
4 x 2.
This is 200.
Now, 200 x 50.
2 x 5.
10.
And.
2 x 0.
1 x 0.
3 x 0.
So, what is our interest?
Simple interest.
In this case, we have.
Rs. 10,000.
This would be our simple interest.
So, it was easy.
You just have to keep this conversion in mind.
That rate of interest is in per annum.
And what should be our time period?
Time period should be in years.
And if I add one more question to this.
You tell me.
After 9 months.
How much sum of money will you get?
Again.
So, what will you get?
How much sum of money will you get?
That is your.
Amount.
So, what will be your amount?
Amount.
Would be.
Simple interest.
Rs. 10,000.
Plus principal.
That is Rs. 80,000.
So, total amount which you will get.
After 9 years.
That would be.
Rs. 90,000.
So, you understood the amount.
And SI.
Simple interest.
You understood.
If.
Like we just did the formula.
S is equal to PRT upon 100.
So, if you.
All of you will do this.
If you want to get simple interest.
Then put the value of PRT.
Divide by 100.
But, if suppose.
We are given simple interest.
And we have to find out from the remaining 3.
So, obviously.
You will find out that unknown.
I am not showing you the relation.
What will be the value of P? SI.
Into 100 by RT.
You will put that in the main formula.
In this main formula.
And whatever will be the unknown.
You will put the given.
And whatever will be the unknown.
You will get automatically.
Okay.
So, now we are moving to the next category.
That is.
If.
If you have.
The amount.
What will be that?
X times the principal.
In some years.
In some years means.
Suppose in T years.
If sum.
Becomes.
If sum becomes.
X.
Times.
The principal.
X times the principal.
In how many years?
In T years.
And what is your SI?
We will denote with SI.
At the simple interest.
So, what will be your sum?
What will be the sum?
And 8% will be given to you.
Rate of interest.
So, if sum is being told to you.
That it is becoming X times the principal.
That is.
Your amount is becoming.
X times the principal. of principle. If we are doing
principle p-let and s, i, r, t are same, then you tell us
what will be your r%? Or suppose we give you another case
that your amount is x times p and r% is given, then find
out time period.
So these two cases will come in your case.
So how will we do this? Let us see.
We have given amount xp.
We got this amount from statement.
So apply SI formula.
What will be SI formula? SI would be p, r, t by 100.
So what will be your amount? SI plus p.
SI plus p would be your amount.
And what is the given amount? xp.
So this is equal to xp.
So if you put values, then what will happen? p, r, t by
100, value of SI plus p is equal to xp.
This is all.
Now what is common term in all three? p, p is common.
So p is cancelled out.
Now what we have to find out? We have to find out r.
So keep r aside and all other things on other side.
So what is this? r, t by 100 plus 1 is equal to x.
If you take plus 1 to other side, then what will happen?
Minus 1.
Now if we take 100 to other side, then we have r is equal
to x minus 1 into 100 divided by t.
This would be your r percentage.
Whatever value will come, you can put percent in front of
it.
Then what will happen? Rate of interest.
If 5 is coming, then 5 percent and if 10 is coming, then we
will write 10 percent answer.
So this is your one case.
When you are told about time period, SI, principal amount,
all these things and what you have to find out? r percent.
Now what is the condition in this? That your amount is some
times, x times, z times, whatever times, of principal
amount.
Means what is the principal amount? It is multiple.
Then how will we find out this? Now what is the second case
of this? That you have to find out r percentage.
What you have to find out? You have to find out time period.
So we will go on this same note.
Now what will happen? You just keep t here.
Keep t aside, whatever we have to find out.
So after this step, I am doing it here.
Keep t aside, rest of the things are on other side.
So what we have t? x minus 1 into 100 divided by r.
This would be our time period in years.
So you understood this case.
So let us do a basic question.
So write the question.
Question would be, at what rate percent per annum sum
will, if we are asked to find out rate percent, and what
will be the sum? Sum will double.
At what rate percent sum doubles in two years? If we are
asked rate percent, obviously per annum they have
mentioned, well and good.
If you are not mentioned per annum, or nothing mentioned,
half yearly, quarterly, then you will assume it as per
annum.
Till you are not mentioned that half yearly rate of
interest or quarterly rate of interest, you will assume it
automatically as per annum.
Sum doubles in two years.
So we have to find out r percentage.
If we are talking about sum doubles, that is what sum is
doubling.
That is amount, if we had something, sum doubles, that is
what amount is doubling, of principal.
It is a kind of solution.
If our sum is doubling, then what is happening? If it is
doubling of principal, then what is the amount of
principal? 2P.
What is the time period? 2 years.
And we have to find out rate percent.
What is principal? We are letting principal as P.
So, let me put it in direct formula. What will be the value
of x in this? It is doubling.
So, value of x will be 2.
So, if you put in last formula, that was, what was your r?
Your r was x minus 1 into 100 divided by t. So, everything
is given. Value of x is 2.
Into 100 divided by t. t is 2. So, what is this? 2 minus 1
is 1. Into 100. 100 by 2. That is 50.
So, what is our r? 50%.
Rate of interest is 50%.
But, if we are not doing it in this way, let me tell you
another logic.
What is the other logic? What is your A? It is twice of P.
And your A is twice of P.
So, what is the value of A? Simple interest plus principal.
So, this is 2P.
This is SI plus P.
So, what is the value of SI automatically?
SI is equal to principal amount.
When it is equal to principal amount, then in SI formula,
SI is equal to PRT by 100.
In this formula, what do you put? Put value of SI as P.
So, that would be P is equal to P.
And what is your r? You have to find out your r.
r into time.
That is 2.
2 years divided by 100.
P into P cancels.
1. 50.
So, what is your r? 50%.
So, you can do it with any of the two methods.
So, in simple interest, you don't have many formulas.
In compound interest, you will get more formulas.
We will do that in next video.
Till then, you solve all the questions of simple interest
using this concept.
Till then, thank you for watching the video.
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