Lesson video

Hello, everyone, my name is Miss Coo and I'm really happy to be learning with you today.

Today, we're going to be looking at percentages, such an important topic, as we use it so much in real life.

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

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

And by the end of the lesson, you'll be able to appreciate the difference between simple interest and compound interest.

So let's have a look at some key words.

Now, interest is money added to savings or loans.

And simple interest is always calculated on the original amount.

Compound interest is calculated on the original amount and the interest accumulated over the previous period.

Today's lesson will be broken into two parts.

First, we're going to look at simple versus compound percentage change, and then we're going to look at simple and compound interest.

So let's make a start on simple versus compound percentage change.

Now let's say Alex is given £80 and he is told he'll get 10% of this £80 every month.

The bar model shows how much extra he receives each month.

For example, we're going to look at January, and February, and March, and we know we're looking at £80 as that original amount.

Then Alex receives 10% of that.

So that means Alex gets £8, because 10% of £80 is £8.

Now in February, we know we're comparing to that original amount of £80.

And we know Alex gets 10% of that, which we also know is £8, so Alex gets £8.

While in March, we're looking back to that original amount, which is £80, and we know he gets 10% of that amount, which is £8.

Once again, Alex gets £8 in March.

Now over the three months Alex has gained £24 on top of his £80.

Now, let's have a look at Jun.

Jun is given £80 and he's told he'll get 10% of the previous month.

I'm gonna show you with bar models how much extra he receives each month.

So we're going to look at the three months again, January, February, March.

Let's have a look at January where we know he has £80 as that original starting amount.

He gets 10%, so that means Jun gets £8 in January.

Now in February, how much does he now have? Well, he has £88, because the previous month is an accumulation of the £80 and that £8.

So he gets 10% of that.

10% of £88 is £8.

80.

So that means Jun gets £8.

80 in February.

But what about March? Let's think what he has from the previous month.

In the previous month he has £96.

80.

So if he receives 10% of that, he gets £9.

68.

That means in March he gets £9.

68.

So in total over the three months, Jun has gained £26.

48 on top of his £80.

These two examples really do illustrate the difference between simple interest and compound interest.

Alex is showing a simple interest, and simple interest is always calculated on the original amount.

We kept on going back to that £80 each month.

Now for Jun, compound interest is the interest calculated on the original amount and the interest accumulated from the previous period.

And you can see that, because originally in January he started with £80.

Then in February it was the £80 plus the £8, and that's what he receives his 10% on.

And in March, once again we're using that original amount and the interest accumulated over the past two months.

These bar models really do illustrate the difference between simple interest and compound interest.

So let's have a look at a check.

Two pupils are told they'll receive 15% interest each month on £120 over two months.

Sofia will receive the simple interest and Laura will receive compound interest.

I want you to fill in the missing information.

On the left, it shows Sofia and on the right it shows Laura.

See if you can copy it down, fill it in, press pause for more time.

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

Well, let's look at Sofia's bar models first.

Well, we know the original amount was £120.

Receiving 15% of £120, means Sophia gets £18 in the first month.

In the second month, now remember she's getting simple interest, so we're referring back to that £120, and then we're looking at 15% of that £120, which is £18.

So that means in total, Sophia gets £18, plus £18, which is £36 in interest.

Now, let's have a look at Laura.

Well, Laura, we know in month one has £120, and then she receives a 15% interest, which we know is £18.

In month two, we're looking at what she has in total from month one.

Well, £120 at £18 is £138.

So then we work out 15% of that amount, which gives us £20.

70.

So in total Laura got £18 in the first month and then £20.

70 in second month, giving a total interest received of £38.

70.

Well done if you got this one right.

Great work, everybody.

So let's move on to our task.

Question one wants you to complete the bar models and total interest when simple and compound interest of 5% per year is applied to £480 over two years.

See if you can give it a go, copy it down, but take your time, and press pause.

Great work everybody.

So let's move on to question two.

Question two says, complete the bar models and total interest when simple and compound interest of 2% per year is applied to £6,000 over three years.

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

Great work.

Let's move on to question three.

Question three's a really tough question, as you're given bits and bobs of information and you have to fill in the missing information, showing a compound and simple interest of the same amount of money.

Take your time with this one, it's quite tricky.

Press pause for more time.

Fantastic work.

So let's go through these answers.

Well, for question one, on the left hand side it shows the simple interest.

Now we know the original amount was £480, 5% of that is £24, so I placed it here.

Now for year two we know the original amount is still £480.

5% of that is still £24.

So that means the total simple interest raised is £48.

Well done if you get this.

For the second part of question one, it wants you to work out the compound interest.

Well, we know for year one we have an original amount of £480.

5% of that is £24.

But in year two, remember we're looking at the accumulation from the previous year.

So that means we have a total of £504 from the previous year, 480 add 24.

5% of our £504 is £25.

20.

So that means the total compound interest is £24, add £25.

20, which gives you £49.

20.

Massive well done if you got this one right.

For question two it wants you to complete the bar models and total interest when the simple and compound interest of 2% is applied to £6,000 over three years.

So let's have a look at the simple interest first.

Well, the original amount we have in year one is £6,000.

And remember, because it's simple interest, that original amount is the same.

So all I've done is put £6,000 in for the original amount for year one, year two, and year three.

I've also identified 2% to be £120 for all of the years, for year one, year two, and year three.

So that means the total simple interest is 120, add 120, add 120, which is £360.

Well done if you at this.

For the compound interest, we know in year one the original amount was £6,000.

2% of that was £120.

Now for year two, remember it's an accumulation of the previous year, so that means in total we have £6,120 from the previous year and we're working out 2% of that, which is £122.

40.

Now in third year, same again, it's an accumulation of the previous year, so it's £6,242.

40.

2% of that is £124.

85.

So that gives us a total compound interest when we're adding up 120, add £122.

40, add £124.

85, gives us a total compound interest of £367.

25.

Massive well done if you got this one right.

For question three, it's a great question.

It's giving you some bits and bobs from a simple and compound interest of the same amount of money.

So let's see what you worked out.

Well, from the previous year we know that the previous year had to be £970.

20.

How did we know that? Well, we knew it because if 5% is £48.

51, that means we could work out the 100% as £970.

20.

Really well done if you got that.

In year two, that means we know the 5% is £46.

20.

So that means the 100% had to be £924.

Massive well done if you got that one.

And year one, well, we can work backwards now because we know the total accumulation was £924.

In other words, that's your 105%.

So if 105% is £924, the 5% is £44, and the original amount was £880.

So that means, adding up the compound interest, we have a total compound interest of £138.

71.

Now the question stated that we're looking at the same amount of money for the simple and compound interest.

So that means for the simple interest, the original amount of money was £880.

5% of that would be £44, So we can work out the simple interest of 5% over the three years of £880 to be £132.

Massive well done if you got this one right.

That was really tricky.

Great work everybody.

So let's move on to the second part of our lesson, simple and compound interest.

There are times where the question does not explicitly say it's simple or compound interest.

As a result, it's important to read the context of the question and determine if the interest is accumulated over the previous period or an interest based on the original amount only.

So let's have a look at some examples.

Here we have a car, and the car is advertised.

Vintage car, £8,000, plus 13% fees.

Spread it over five years, so it's £151 per month.

Now I want you to have a little think, do you think it's simple interest, compound interest, or neither? And I want you to explain how you know.

See if you can give it a go.

Press pause for more time.

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

Well, it's simple interest, as you are paying 13% of the original amount, which is just £8,000, then that is just simply spread over the five years.

Well done if you got this.

Let's have a look at another question.

Andeep has £400 in his account.

The bank offers 1.

2% interest of what is in the account at the end of every month.

He does not withdraw any money for five months.

Do you think this is simple interest, compound interest, or neither? Well done.

Well, hopefully you spotted its compound interest, because he's receiving interest on the previous accumulated amount, which is received interest.

Well done.

Now let's have a look at a slightly different example.

It's still looking at Andeep and £400 in his account, and the bank is still offering that 1.

2% interest of what's in the account at the end of every month.

However, at the start of each month, Andeep withdraws the interest received.

Now do you think he's receiving simple interest, compound interest, or neither? Well, he's receiving simple interest, as he's only receiving interest on the original amount of what was in his account, as he's withdrawing the accumulated amount, making sure that the original amount is the same each month.

Well done if you got this.

Great work everybody.

It's really tricky to know if you have a simple interest question or a compound interest question.

Just remember, simple interest is the interest calculated on the original amount and compound interest is the interest calculated on the original amount and the interest accumulated over the previous period.

So now what I want you to do, I'd like you to start your task.

Identify if the following uses simple interest, compound interest, or neither? Try and remember those definitions.

For question 1A, it says, a customer owes a shopkeeper some money.

The shopkeeper says the customer will pay an extra 1% on what is owed for every day that passes until it's paid back.

What do you think? Simple interest, compound interest, or neither? For B, a holiday costs £1,290, and then you've got an additional 15% fees.

The cost is then spread over 12 months.

Do you think this is simple interest, compound interest, or neither? And for C, a customer owes a shopkeeper some money again.

The shopkeeper says the customer will pay an extra 10p on what is owed for every day that passes until it's paid back.

What do you think? Simple interest, compound interest, or neither? See if you can give these a go.

Press pause one more time.

Great work.

Let's move on to question two.

Question two shows an image from a spreadsheet.

Does it show a compound interest or a simple interest? And I want you to explain how you know.

Just so you know, the little asterisk represents a multiplication.

So in cell D2 when it says B2*1.

05, that means the quantity in cell B2 is multiplied by 1.

05.

This is a tricky question, see if you can give it a go.

Press pause for more time.

Well done.

Let's move on to question three.

Question three shows an image from another spreadsheet.

Now, does it show a compound interest or simple interest? Explain how you know.

Remember that asterisks means a multiplication.

So for example, in cell D2 it says the amount in cell B2 is added to the amount in B2 multiplied by 0.

05.

This is a tricky question again.

See if you can give it a go.

Great work.

Let's move on to these answers.

Well, for question 1A, it's compound interest.

Really well done if you've got this.

It's because the shopkeeper is accumulating the interest from the previous day.

For B, it's a simple interest.

We're just adding 15% of that original amount and then spreading it over the 12 months.

Well, for C, it is neither, because the 10% is simply just added on each day.

The only way that this could be a simple interest is if the 10p represents a percentage of the original amount.

Well done if you got that one.

For question two, does it show a simple interest, compound interest, what do you think? Well, it shows a compound interest, and the reason why it shows a compound interest is because the end of the year amount is actually shown in column D.

And the start of the year amount is referencing column D and increasing this by 5%.

So you can see the multiplier of 1.

05 indicates that it's an increase of 5%.

So in cell D2, that's the amount accumulated at the end of year one.

Now in cell D3, you'll notice it's referencing cell B3.

B3 is the total from the previous year, as it's referencing cell D2.

This was really tough.

A huge well done if you've got this one right.

Let's have a look at question three.

Question three, do you think it shows a compound interest or simple interest? Well, it shows a simple interest.

Well, in cell D it references the end of year amount.

So the end of year amount is only increasing by £400 each year, in other words, cell B2.

You can constantly see that reference of cell B2 in that column D.

Given the fact that B2 is being multiplied by 0.

05, this means there's a 5% interest added each time from the original amount, which is cell B2, which is £400.

So that means it's a simple interest.

Massive well done if you understood this formula.

Great work everybody.

So we know simple interest is interest calculated on the original amount and we know compound interest is the interest calculated on the original amount and the interest accumulated over the previous period.

In this lesson, we've used bar models to illustrate how simple and compound interest are seen.

There are times where the question doesn't explicitly say it's compound or simple interest.

So it's important to read the context of the question and determine if it is simple interest, compound interest, or neither.

I think this lesson is probably one of the most important lessons in mathematics, because we use it so much in real life.

You'll come across simple interest or compound interest when you are looking at loans, credit cards, bank accounts, so many different forms. I really do hope you've enjoyed this lesson.

Massive well done, great working with you.