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 and welcome to today's lesson on simple interest calculations with technology and it's under the unit, percentages.

By the end of the lesson, you'll be able to carry out simple interest calculations with a calculator.

Let's have a look at some key words starting with interest.

Now remember, interest is money added to savings or loans.

We'll also be using the words, simple interest and simple interest is always calculated on the original amount.

It's always good to know what compound interest is in comparison to simple interest and compound interest is calculated on the original amount and the interest accumulated over the previous period.

We'll also be using the word, the rates of interest.

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

Today's lesson will be broken into two parts.

We'll be looking at calculating simple interest first and then finding the original amount second so let's make a start.

Now, we'll be using the Casio FX-570 or 991 class width to find a percentage.

Remember, scientific calculators are fantastic tools but they only give the correct answer if the input is correct.

Therefore, it's important to carefully input a calculation so it'll give the correct output answer.

Now bar models are efficient ways to show simple interest.

For example, this bar model shows an amount of 780 pounds was invested for four years at a simple interest rate at 2% per year.

Now looking at this question, see if you can work out the 2% simple interest.

Hopefully, you've worked it out to be 780 multiplied by 0.

02, which is 15 pound 60.

So that means we know our 2% interest is 15 pounds 60.

Now given that 2% represents 15 pound 60, how much is in the account after the four years? See if you can have a little think.

Well, it would be our 780 pounds, which was our original amount, add the four lots of our 15 pound 60, which is 842 pound 40.

Now what I want you to do is let's check this understanding.

Using this bar model, work out the total amount when 890 pounds is invested for five years at a simple interest rate of 4.

3%.

See if you can give it a go.

Press pause if need more time.

Great work! Let's see how you got on.

Well, each 4.

3% is found by 890 multiplied by 0.

043, which gives me 38 pounds 27.

If you weren't quite sure how to find out what 4.

3% is as a decimal equivalent, you simply divide the percentage by a hundred.

Since 4.

3% represents 38 pounds 27 and there are five years, that means we simply do 890 pounds, add our 38 pounds 27, multiply by five gives us our 1081 pounds and 35 cents.

Well done if you got this one right.

Now, it's important to remember there's another way to calculate the final amount when 780 pounds is invested for four years at a simple interest rate of 2% per year.

It's simply 780 multiplied by 1.

08, which gives us the same amount, 842 pounds and 40 pence.

But can you explain why 780 multiplied by 1.

08 shows a simple interest at 2% over four years? Have a little think.

Well, it's because if you know each year there's a 2% increase and it's over four years, that means there's an 8% increase.

Therefore, it's the same as increasing 780 pounds by 8%.

Now what I want you to do is I want you to use multipliers to work out the total amount when 950 pounds is invested for five years and a simple interest rate of 5.

1% per year.

See if you can give it a go.

Have a look at that bar model and press pause for more time.

Great work.

Let's see how you got on.

Well, you know, overall the bar model shows 125.

5%.

So that means we simply multiply 950 by 1.

255 to give me 1,192 pounds and 25 pence.

Well done if you use multipliers to work this out.

An alternative is to use the formula and to input the correct values when 780 pounds is invested for four years at simple interest at 2% per year.

Remember the formula to work out the total is P add T times P times R, where P is the original amount, T is the time and R is the interest rate as a decimal.

So let's plug in our values, 780 add four times or 780 multiplied by that interest rate as a decimal, which is 0.

02.

It gives us exactly the same answer as before, 842 pounds and 40 pence.

Now what want to do is have a look at this question and see if you can give it a go.

An Oak teacher invests 954 pounds for eight years into a savings account and the account pays simple interest at a rate of 3.

5% per year.

We're asked to work out the total amount in the account at the end of the eight years.

See if you can give it a go.

Press pause if you need more time.

Great work.

Let's see how you got on.

Well, I'm gonna use the formula first, P add T times P times R.

Plugging in our values, I know the original amount was 954, add the eight years multiplied by our 954 times our percentage rate as a decimal, 0.

035.

This gives me an answer of 1,221 pounds and 12 pence.

Well done If you got this, you may have done it another way, but hopefully you would've still got the right answer.

So regardless of the approach you use to answer a simple interest question, make sure you read the question carefully.

You need to know if you need to calculate the total amount after the interest has been added or the total interest only.

There are a number of different ways you can use your calculator to work out the final total after a simple interest rate over a period of time, bar models, multipliers, and obviously our formula as well.

Now when we're asked to work out the simple interest only, you don't add the original amount after finding the total interest.

So you can see this in the bar model.

We're just asked to work out the interest.

Using multipliers, we're only asked to work out that percentage interest and using the formula, we're not adding on the original amount.

Let's have a look at a check.

Aisha has 184 pounds for three years in a savings account and the account pays simple interest at a rate of 1.

34% per year.

How much does Aisha have in the account after three years? See if you can give it a go.

Press pause one more time.

Well done.

Let's see how you got on.

Well, I'm gonna use multipliers.

We know 1.

34% each year for three years is an increase of 4.

02%.

So that means I simply do my 184 pounds multiply by 1.

042 as it's an increase of the 4.

02%.

This gives me 191 pounds 40, to two decimal places, as it's money.

Alternatively, you could have used the formula.

Remember it's P add P times T times R, so it's 184 add three times 184 times 0.

0134, giving me exactly the same answer.

Let's have a look at another check.

In this question though, it wants you to work out the total interest only when 1,290 pounds is invested for six years in a savings account.

The account pays simple interest at a rate of 2.

35% per year.

See if you can give it a go.

Press pause one more time.

Fantastic work.

Let's see how you got on.

Well I'm going to use multipliers and remember, 2.

35% each year for six years is an increase of 14.

1%, but the question only wants us to work out the total interest.

So, we simply multiply our 1,290 pounds by the 0.

141, which is the interest only, giving me 181 pounds and 89 pence, to two decimal places.

You could use the formula.

Notice how the formula, we're not adding P as the original value.

So it's simply T multiply by P multiply R, which works out to be six times 1,290 times 0.

0235, which gives us the same answer.

Great work if you've got these.

Fantastic work everybody.

So let's move on to your task.

Read the questions carefully.

Make sure you know if you need to work out the the total amount after the simple interest or if you're only asked to work out the total interest.

See if you can give it a go.

Press pause for more time.

Fantastic work everybody! Let's move on to question three and four.

Same again.

Read that question carefully.

Press pause for more time.

Great work.

Let's move on to question five.

Match each calculation to the question and the correct answer.

See if you can give it a go.

Press pause one more time.

Amazing work everybody.

Let's look at our last question, question six.

An Oak teacher buys a car for 12,000 pounds at a simple interest rate of 2.

3% per month.

Each month the teacher pays 500 pounds from what is owed and is charged a simple interest rate at 2.

3% of the 12,000 pounds only.

How many months will it take for the Oak teacher to pay for the car completely? Great question.

Real life applications here.

Let's see how you get on.

Press pause for more time.

Wonderful work everybody.

Let's go through these answers.

Well, for question one, there's lots of different ways to work it out.

For me, I've used multipliers giving me, 250 pounds and 85 pence in the account after three years.

And for question two, I prefer to use multipliers again to give me 36 pounds is the total interest after four years.

Press pause if you wanna have a look at that working out a little bit more.

For question three and four, well I'm going to use multipliers again to give me 403 pounds and 45 pence for question three.

And using multipliers for question four, it gives me an answer of 479 pounds and 91 pence.

Press pause if you wanna have a look at that working out a little bit more.

Well done.

Question five, hopefully you've matched these.

Massive well done if you got this one right.

Press pause if you need.

Lastly, question six, great question.

Each month the teachers charge 2.

3% of the 12,000.

That means the teacher's being charged 276 pounds per month.

Considering the teacher pays 500 pounds a month, that means each month the teacher's only paying off 224 pounds per month.

So working out how much the teacher's paying off, we simply do 12,000 divided by 224 pounds, which means it's going to take 53.

6 months, to one decimal place, to pay off the car.

So that means it's gonna take 54 months in total to pay the car off.

Great work if you've got this.

Fantastic work everybody.

So let's move on to the second part of our lesson, finding the original amount.

We can use a bar model to visualise the total amount after simple interest has been added.

For example, here's a simple interest rate of 5% per year and it's applied to 900 pounds over four years.

From here, you can see this in a lovely little bar model.

Now I want you to look at this and think what percentage does the total amount represent after four years? Have a little think.

Well hopefully you can spot the bar model really does show 120%.

The original is a hundred percent and we have four lots of 5%.

And we can represent this in a ratio table as well knowing that a hundred percent is 900 pounds.

So that means multiply by 1.

2 gives me my 120%, which you can see in our bar model.

And this gives me a total of 1080 pounds.

So after four years, a simple interest rate of 5% per year, we know there is 1080 pounds in the account.

Ratio tables are fantastic as they'll allow us to work out the original amount given that we know the total amount.

So given this ratio table and bar model, you can see your 120% is 1080 pounds.

How do you think we can go back and calculate what the original amount is? Using that ratio table, hopefully you've spotted, you simply multiply by 100 over 120 or divide by 1.

2.

Doing that, it gives me an original amount, which is 900 pounds.

Great work.

Let's have a look at a check.

A simple interest rate of 3.

2% per year over four years gives us a total amount of 631 pounds 68 pence.

Put the information from our question into a ratio table and work out the original amount.

See if you can give it a go.

Press pause for more time.

Fantastic work everybody.

Let's see how you got on.

Well we know in total, the entirety is seen in the bar model to be 112.

8%, which is 631 pound 68 from our question.

That means in a ratio table, we know 112.

8 is equal to 631 pound 68.

So how do we go back and work out the original amount? Well, we simply multiply by a hundred over 112.

8.

This will give me my a hundred percent, which is 560 pounds.

So that means 560 pounds was originally in the account.

I also want to show you how we can use multipliers.

For example, after four years, at a simple interest rate of 5% per year, we know there is 1080 pounds in the account and we're asked to work out how much was invested.

Have a little think.

Well let's recognise the fact that we know 120% is our 1080 pounds because we know each year it increases by 5%.

So that means we know there's a 20% increase giving us 120% represented as 1080 pounds.

So let's write this as a calculation.

120% of what gives us 1080? Well converting 120% into our multiplier, that's the same as 1.

2 times what gives us our 1080? Dividing identifies that original amount (indistinct) to be 900 pounds.

Well done if you spotted this.

It's all about recognising that multiplicative relationship between our numbers.

So we know the original amount was 900 pounds.

Now what I want you to do is using multipliers work out the original amount when a simple interest rate of 1.

9% per year over three years gives a total amount of 930 pounds and 16 pence.

See if you can give it a go.

Press pause one more time.

Well done.

Let's see how you got on.

Well we know in total, it's 105.

7% because we have three years each accumulating 1.

9%.

So let's see, we can write it using multipliers.

105.

7% of our original value gives us 930 pounds and 16 pence.

Converting into a decimal, remember that quick little weigh, you simply divide the percentage by a hundred, gives us 1.

057 multiplied by our original amount equals 930 pounds and 16 pence.

Dividing gives us the original amount, which is 880 pounds.

Multipliers are great and efficient ways to work out the original amount.

Well done if you got this.

So using any method you like really work out the original amount when a simple interest rate of 3.

45% per year over seven years gives a total of 1,489 pounds and 80 pence.

So 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 use a ratio table first and then illustrate with multipliers.

Using a ratio table 3.

45% each year over seven years gives a total of 124.

15%.

So that means I know that percentage represents our total amount.

To work out a hundred percent, I multiply I by a hundred over the 124.

15 giving me the original amount to be 1,200.

Really well done if you got this.

I'm going to now use multipliers.

If we're receiving 3.

45% per year over seven years, there's an increase of 24.

15%.

So that means our original value multiplied by 124.

15% gives us that 1,489 pounds and 80 pence.

Converting to a decimal, I have 1.

2415 times the original amount and that means I can simply divide giving me exactly the same answer.

Great work if you've got this and which method do you prefer? Great work everybody.

So let's move on to your task.

I want you to fill in the table to give the original amounts invested.

See if you can give it a go.

Press pause for more time.

Well done.

Let's move on to question two.

Question two, you want to make a million pounds from 500,000 pounds investment and you plan to invest the money for several years at a simple interest rate, which is less than 6%.

Find three different interest rates and time periods to make the million pounds.

See if you can give it a go.

Press pause for more time.

Well done.

Let's move on to these answers.

Well here are all our answers to question one.

Fantastic work.

Press pause if you need more time.

Okay, well done everybody.

Let's have a look how we can make a million pounds from 500,000 pounds.

There are an infinite number of examples, but what's important to remember is the interest needs to be 500,000 pounds.

In other words, you have the original amount in your account and the interest of 500,000 pounds will give us our million.

So therefore, the rate multiply by the number of years multiply by 500,000 pounds must be 500,000.

So therefore we know the number of years multiply by the rate must equal one.

So for example, if you had 500,000 pounds in your account at a simple interest of 5% for 20 years, that will get you the interest of 500,000 pounds because we know 20 years times 0.

05 is equal to one.

Another example would be a simple interest rate of 4% for 25 years because 25 multiply by 0.

04 is equal to one.

Another example would be 2% simple interest rate for 50 years.

50 times 0.

02 gives us our one.

These are three examples of how you can get million pounds having 500,000 pounds in your account.

Well done and remember there's an infinite number of examples here, but as long as when you multiply the number of years by the rate, it equals one, that's the only way in which you can get a million pounds with an original investment of 500,000 pounds at a rate which is less than 6%.

Well done.

Excellent work everybody.

So in summary, there are a number of different ways you can use a calculator to work out the final total after a simple interest rate is applied over a period of time.

For example, bar models, multipliers or even a formula.

The original amount after simple interest is added can be found by using ratio tables and reverse multipliers.

And finally, it's important to read the question carefully so you know the total amount after the simple interest is required or only the total interest.

Great work everybody.

I hope you've enjoyed the lesson.

It was wonderful learning with you.