Lesson video

Hi everyone.

My name is Ms Coo, and I'm really happy to be learning with you today.

In today's lesson we'll be looking at percentages, and percentages is so important as they appear so much in everyday life.

I really hope you enjoy the lesson, so let's make a start.

Hi everyone, welcome to this lesson on simple interest calculations under the unit percentages.

And by the end of the lesson you'll be able to carry out simple interest calculations.

So let's have a look at some keywords that you'll see a lot during the lesson.

First keyword is rate of interest.

Now the rate of interest is the percentage by which an amount increases.

We'll also be looking at the word interest.

Remember, interest is money added to savings or loans.

Simple interest is always calculated on the original amount, and compound interest is calculated on the original amount and the interest accumulated over the previous period.

But we'll be looking at simple interest today.

So our lesson will comprise of two parts, calculating simple interest and then finding the original amount.

Let's work on calculating simple interest.

Firstly, we can simplify simple interest into one bar model.

For example, these bar models show how much simple interest Alex receives over three months.

We have January and we know Alex gets this original amount.

Then he gets 10% of that, so that's five pounds.

So that means we know in January, Alex gets five pounds.

In February, Alex has the same original amount.

He gets 10% of this and that means in February, we know he gets five pounds.

In March, Alex still has the original amount of 50 pounds.

He still gets 10%, which is five pounds.

So what we're gonna do is we're going to simplify these three bar models showing the interest received over three months into one nice bar model.

To do it, we just need to use the knowledge that simple interest is the same amount and we can change the bar model to show the same interest rate and time period in one simple bar model.

So for example, you can see the original amount is 50 pounds here.

We have January displayed as 10%, which is five pounds.

February is 10%, which is five pounds, and March, which is 10%, which is five pounds.

So we can now see the simple interest and the total in the account in one efficient bar model.

So let's have a look at another example.

Let's say you had 480 pounds in a bank account and it's increased by 5% in one year.

How much do you think you have after one year? Have a little think about what this bar model looks like too.

Well done, let's have a little look.

Well, if you have an increase of 5% in year one, that means we have an extra 24 pounds, and that illustrated the 5% here.

Now let's say we have year two and assuming no withdrawals in year two, you receive another 5% of what is originally in your account.

How much do you have in your account and what do you think the bar model looks like? Well done, well you'll have another 24 pounds because it's another 5% and you can see I've illustrated it here.

So that means you have in your account 480 and 24 and 24, which is 528 pounds.

What about year three? What do you think that looks like and how much do you have in your account now? Well it's going to look like this because you can see those three, 5% illustrating what you receive each year.

So that means in total you have 552 pounds.

What do you think the bar model and calculation would be to work out how much you'll have in your account given 480 pounds receives a simple interest of 5% per year over six years? See we can have a little think.

Press pause for more time.

Great work, let's see how you got on.

Well, for six years this would represent six lots of our 5%.

So that means working this out, it's our original amount, which is 480 pounds, add six lots of 24 pounds, which works out to be 624 pounds.

Well done if you've got this.

You can see from our calculation that each 24 pounds is the amount received in a year.

So let's see if we can simplify the calculation further.

We know we have 480 pounds, add six lots of our 24, as we know it's 624 pounds.

And I want us to break this calculation down a little bit more.

Let's look at it and understand what each part of it represents.

Let's look at our 480 pounds.

From the context of the question, what did this represent? Well, it represented our original amount.

And the six represented the number of years, in other words, the time.

And the 24 pounds represented the interest from the original amount.

Now let's look more into how we worked out this answer.

What is the calculation to work out 5% of 480? Well, one method would be 480 multiplieded by 0.

05.

So I'm going to replace that 24 pounds with that calculation.

480 multiplieded by 0.

05, all I've done is replace that amount with this calculation.

Now we can see using this example how we can generate a formula to calculate the total given an original amount, time period, and simple interest rate.

Because this calculations highlighted in yellow really does show the interest from the original amount.

And this formula is given as P add T, multiply by P, multiply by R, where P is the original amount, T is the time, and R is the interest rate as a decimal.

This formula is fantastic as it tells us the total amount of what's in our account.

But if we were only asked to work out the total interest after a certain amount of time, then we simply do T multiply by P, multiply by R.

So once a calculation is formed, we can work out either the total amount or the total interest, without a calculator and using knowledge on the associative law or we can use a ratio table.

So just remember and read the question carefully.

If it's asking you for the total amount, you can use the formula P add T times P times R, and if the question wants you to work up the total interest, it's T multiplieded by P multiplieded by R.

So let's have a look at a check.

In this example, we can work out the answer to this question using the associative law or ratio table to find the interest as an amount.

I'm gonna show you both methods.

The question says Aisha has 400 pounds for five years in a savings account, and the account pays a simple interest rate of 3.

5% per year.

How much does Aisha have in her account after five years? So let's see if we can work out that simple interest.

Well, we know a hundred percent represents the 400 pounds.

So I'm going to divide by a hundred to give me 1%.

So that means 1% is four pounds.

Now because she gets 3.

5%, I'm going to multiply by three.

So I know 3% is 12 pounds, and I'm gonna divide that 1% by two to give me 0.

5%, which is two pounds.

So that means summing the 3% and the 0.

5% gives me 3.

5%.

So that means I get 3.

5% is 14 pounds.

So that's the simple interest she receives each year.

Now given that she receives that interest for five years, it's 400 pounds, add five times 14, which is our 470 pounds.

Now let's move on to using the associative law.

So to find the total amount, I'm going to use that formula P add T times P times R.

Well we know P was the original amount, add T was the time, which is in years, multiplieded by P, which is our 400, multiplieded by the rate as a decimal is 0.

035.

So I'm going to work this out now, 400 add five, well I know five times 400 is 2000, multiply by 0.

035.

Using my knowledge on the associative law, I'm just gonna simplify this a bit.

400 pounds add 200 pounds times 0.

35, which is the same as 400 pounds add 20 pounds times 3.

5, which is the same as 400 pounds, add two pounds times 35, which is the same as 400 pounds, add 70 pounds, which is 470 pounds.

Notice how we get the same answer.

I've just used the associative law here and before we used to ratio table.

So after curiosity, which do you prefer, the associate of law or using the ratio table? Both have their advantages and disadvantages and it does depend upon the difficulty of the question too.

Regardless of the approach, finding the percentage is important as you can work out the interest as an amount and multiply it by the stated amount of time.

Great work everybody.

So let's have a look at a check.

Sam has 580 pounds for three years in a savings account and the account pays simple interest at a rate of 2.

5% per year.

How much does Sam have in the account up to three years? Choose any method you prefer, press pause as you'll need more time.

Great work everybody.

So let's see how you got on.

First of all, I'm gonna use the associative law.

So using the associative law on the formula, I know the question wants me to work out how much does Sam have in total after the three years? So that means P add T times P times R, substituting in my values I have this calculation, and I'm going to use my associated law just to simplify it to give me a total answer of 623 pounds and 50 pence in the account.

Lots of different ways you could have used the associative law.

I've chosen to this one as I found it more simple.

Alternatively, you may have used a ratio table.

Well if you know a hundred percent is 580 pounds, I'm gonna work out 10%, which is 58 pounds.

So that means if I divide it by two, I've got 5%, which is 29 pounds, and dividing by two again is 2.

5%, which is 14 pounds 50.

So now I've worked up my 2.

5%.

I simply multiplieded by the number of years to give me exactly the same answer.

Same again, you may have found 2.

5% in a different way using the ratio table, but you would've still got the same right answer.

Let's have a look at another check question.

Here, the question wants you to work out the interest only when 600 pounds is invested for four years in a savings account and the account pays simple interest at a rate of 1.

5% per year.

See, you can give it a go, press pause for more time.

Great work, let's see how you got on.

While using the associative law, remember, we're only interested in the total interest.

So that means it's T multiplied by P, multiply by R.

This works out to be four, multiply by 600, multiplied by T 0.

015.

Working this out using the associative law, I've worked out my answer to be 36 pounds interest.

Now notice how I've applied the associative law in this way.

You may have used a different approach, but hopefully you still would've got a 36 pound interest.

Well done.

Alternatively, you could have used the ratio table.

Knowing a hundred percent to 600 pounds, I'm going to work at 1%, which is six pounds, then 0.

5% and then add them together to give me my 1.

5%, which is nine pounds.

So that means I know the total interest is four times nine, which is 36 pounds.

Great work everybody.

So now let's move on to your task.

These calculations work out the total interest given P, which is the original amount, T, the term in years, and R, the simple interest rate as a percentage.

From the calculations can you extract what is the value of P? What is the value of T? And what is that simple interest rate as a percentage? So you can give it a go, press pause one more time.

Well done, let's move on to question two.

Question two gives you calculations for the total amount.

From these calculations can you identify what P is, T is, and the interest rate as a percentage? See if you can give it a go, press pause one more time.

Well done, let's move on to question three and four.

Read question three and four carefully and make sure you know the difference.

If the question is asking you to work out the total or the total interest only.

See if you can give it a go, press pause for more time.

Great work everybody.

Let's go through these answers.

Well here are answers for question one.

Press pause if you need more time to mark them.

Really well done, especially if you've got that last one that was quite tricky.

For question two, here are all our answers again, well done if you've got these, press pause if you need more time to mark them.

Really well done as some of these were quite tricky as they were decimal percentages.

For question three, did you read the question and know if you are calculating the total interest only or the total amount? Well question three was asking for a total amount, which was 265 pound 20.

And for question four it only wanted the total interest, which was 90 pounds, well done.

Great work everybody.

So let's have a look at the second part of our lesson, finding the original amount.

Given we know the amount of interest is the same after a certain amount of time, we can simplify the bar models.

For example, let's show the total amount when simple interest of 5% per year is applied to 900 pounds over four years.

Well we know we have the original amount of 900 pounds, and we know in year one we get 5%, which is 45 pounds.

That means we have a total amount after year one to be 945 pounds because it was 900 add one times our 45.

Now in year two the calculation is 900, add two times 45, which is 990.

In year three, 900 add three times 45, which is 1035.

And in year four it's 900 add four times our 45, which is 1080.

So what I'm going to do is represent the following information into a ratio table.

And I'm gonna hide some information.

For example, let's imagine the simple interest was unknown, but the amount of interest was known.

We can put this in our ratio table and then we can work out the simple interest.

Well how do we do this? Well, we know the original amount is 900 pounds.

So if we have an amount of 45 pounds, that means I know 900 divided by 20 would give me that 45 pound interest.

So I have to do the same to the percentage, one hundred divided by 20, which is 5%.

So I can figure out what the interest is by using our ratio table, and it applies in the same way.

Let's say if the amount of interest was unknown but the simple interest was known, we can put this in our ratio table and work out the amount of interest.

So you can see here, I don't know what the amount is, but I do know there's a 5% interest.

So that means to work out the 5%, I simply divide by 20, which I know is 45.

Now let's pretend the original amount isn't known, but we do know the simple interest rate and we know the amount of interest.

The ratio table can help us work out the original amount.

So you can see from our ratio table, I know 5% is 45 pounds, so that means multiplying this by 20, I can find my original amount.

So you could see how powerful ratio tables are as they allow you to find unknowns given certain pieces of information.

So let's have a look at a quick check question.

Here I want you to use the bar model to work out the missing information.

Looking at the bar model, do you know the original amount of money? Do you know how many years are represented in the bar model? What's the simple interest rate? And how do you think you can find the total amount? See if you can give it a go, press pause one more time.

Great work, let's see how you got on.

Well, I'm going to put this in a ratio table.

I know a hundred percent is the original amount, 50 pounds.

So that means 4% can be found by dividing by 25, so I know the interest received is two pounds.

So now I can start filling in my bar model.

So from this I can fill in those missing values.

The original amount is 50, the number of years is three, the simple interest is 4%, and the total amount is 56 pound.

Really well done if you got this.

Let's have a look at another question.

From our bar model can you identify the original amount, the number of years, the simple interest rate, and the total the amount? See if you can give it a go, press pause for more time.

Great work, let's see how you got on.

Well, using a ratio table, we know a hundred percent is 60.

What does that three pounds represent? Well, to work out what three pounds is, is a percentage we divide by 20.

A hundred divided by 20 gives me 5%.

So now I have enough information to finish my bar model.

I know each of these represents 5%.

The original amount is 60 pounds.

The number of years is four, the simple interest is 5%, and the total amount is 72 pounds.

Great work if you've got this.

Let's have a look at a slightly harder question.

In this bar model it shows you some information.

Can you work out the original amount, the number of years, the simple interest rate, and the total amount? See if you can give it a go, press pause one more time.

Great work, let's see how you got on.

Well, using a ratio table, we know 2% is eight pounds.

So how do we work out that original amount? Well, we multiply by 50, giving those a hundred percent is 400 pounds.

So now I know my original amount, I know my number of years, the simple interest rate, and I can work out the total amount, which is 440.

Great work if you've got this.

Let's move on, and still referring to that past question, what do you think the percentage of the whole bar model is? Well, the whole bar model represents the 110%, and the percentage after a hundred percent is divided by the time given the simple interest rate.

Therefore, you can find the original amount given the final total after the simple interest has been added.

So I wanna look at an example.

We're asked to find the original amount when the total amount is 440 pounds after five years at a simple interest of 2%.

So what does that mean? Well it means as we know, each year we get 2%.

So for five years, that means we get a total of 10%.

So that means the entire bar model has to represent 110%.

So 440 pounds is 110%.

Using a ratio table, I've inserted my 110% is 440 pounds.

Dividing by 11 means I've got 10%, which is four pounds.

So I know the original amount, which is a hundred percent is 400 pounds.

Bar models are fantastic illustrations to show the total percentage as a total amount, and ratio tables allow you to calculate what that original amount was more efficiently.

Now let's have a look at a check.

Find the original amount when the total amount is 288 pounds after four years at a simple interest of 5%.

See if you can give it a go, press pause for more time.

Great work, let's see how you got on.

Well, we know this represents our four years.

So in total we know four years where each year gets 5%, that means there's a total of 20%.

So 288 pounds has to be 120%.

Using my ratio table 120% is 288 pounds.

I need to find out what a hundred percent is 'cause that was the original.

So I'm gonna divide by six here.

You can divide by any number.

For me, I just think it's a bit easier because we're finding 20%.

Then I'm gonna multiply by five to give me a hundred percent, so the original amount was 240 pounds.

Well done if you got this.

Great work everybody.

So what I want you to do now, I want you to do your task, see if you can use these bar models to fill out the missing information.

Press pause for more time.

Great work, let's move on to question two.

Same again, see if you can fill in this missing information.

Question three also wants you to fill in some missing information.

Press pause for more time.

Fantastic, moving on to question four.

Can you find the original amount when the total amount in a bank account is 600 pounds after four years at a simple interest of 5%? So you can give it a go, press pause for more time.

Well done, let's have a look at five and six.

Read that question carefully, draw any bar models or ratio tables to help.

Press pause for more time.

Excellent everybody.

So let's move on to these answers.

For question one, I've used a ratio table to find out what 4% represented and then from here I can work everything else out.

Well done if you've got this, press pause if you need more time to mark.

For question two same again, I've used my ratio table to work things out from here.

Here are my answers.

Press pause if you need more time to mark.

Great work, question three, using my ratio table I filled it in accordingly, and here is my information.

Well done if you've got this.

Question four, we've got lots of information here.

So remember, four years where each year receives 5% means it's 120% illustrated in the bar model.

Working this out, I know 100%, which is the original amount is 500 pounds.

Well done if you got this.

For question five and six here are our answers, Massive well done if you've got this.

Excellent work, everybody.

So in summary, calculating simple interest can be done in a number of ways.

In this lesson, we've used bar models, ratio tables, and a formula to help us calculate the total interest or the total amount after simple interest rates.

Showing simple interest in a bar model allows the interest to be seen quickly and easily.

But remember, using those ratio tables also allows you to use that multiplidcative relationship to find unknown original amounts, simple interest rates, and or the amount of interest.

Massive well done everybody.

It was a tough lesson, but great learning with you.