Lesson video
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Hello, my name is Mr. Clasper.
And today we're going to be learning how to use repeated percentage increases.
Let's have a look at this example.
Increase 34 by 10%.
Now, if we say this bar is worth 34 and it's our starting amount and our original amount, we can say that it also represents 100%.
If we increase this by 10%, that means we have an extra 10%.
And altogether, this would mean that we have 110%.
Now remembering that 110% is equal to 1.
1, or dividing your percentage by 100 will give us 1.
1.
We could calculate 34 multiplied by 1.
1, as this would help us find 110% of 34.
And this would give us a value of 37.
4.
That means that 34 with a 10% increase would be 37.
4.
Let's try this example.
Increase 34 by 10% then by 20%.
In the previous example, we already increased 34 by 10%.
So we multiplied 34 by 1.
1.
And that gave us an answer of 37.
4.
What we then need to do is to take this new amount and increase this by 20%.
So 100 plus 20 would give us 120% in total, which would be a decimal of 1.
2.
So we can take our new amount and multiply it by 1.
2, which gives us a final answer of 44.
88.
Although this is correct, there is a more efficient way to carry out this calculation.
Let's have a look again.
The first thing we did was 34 multiplied by 1.
1, which gave us an answer of 37.
4.
Our next step was to take the new amount and multiply this by 1.
2, which gave us our 44.
88.
However, 37.
4 is equivalent to 34.
11.
So we could calculate 34 multiplied by 1.
1, or increasing by 10%, then multiplied by 1.
2 or increasing by 20%.
And this gives us the same answer of 44.
88.
Let's try this example.
Increase 425 by 20% then by 30%.
An increase of 20% would represent a percentage of 120%.
And this is equivalent to a decimal of 1.
2.
An increase of 30% would represent a total percentage of 130%.
And this is equivalent to 1.
3.
So our calculation would be 425 multiplied by 1.
2 multiplied by 1.
3.
And this gives us 663.
Therefore our final answer is 663 grammes.
Let's try this question.
Answering A, B, C, or D, can you identify the correct answer? Pause the video to complete this task and resume once you're finished.
Did you get it? The correct answer is C, 1.
08.
So if we take our percentage and divide it by 100, we get our decimal, which is 1.
08.
Here are some questions for you to try.
Pause the video to complete your task and click resume once you're finished.
And here are your answers.
So just look out for question number two.
Remember we're multiplying by 1.
05 and 1.
02.
Not 1.
5 and 1.
2 as this would give us an increase of 50% followed by 20%.
So just be careful with that one.
And for question three, we can see our two incorrect answers are 500, multiplied by 1.
2, as this would increase by 20%.
But that's not the same as increasing by 10% followed by another 10%.
And for the last one 500 multiply by two multiply by 1.
1, this would effectively be equivalent to 500 multiplied by 2.
2, which would actually be a total increase of 120%.
Here's a question for you to try.
Pause the video to complete your task and click resume once you're finished.
And here are your answers.
So, if we take a look at this, Amir is actually multiplied by 1.
5, which would increase by 50% and not 5%.
So he needed to multiply by 1.
05 to get his correct answer.
And then multiplying correctly, this should give us 519 pounds 75 pence.
Let's try this question.
An investment is worth 13,000 pounds.
It's increases by 17% every year.
What will the investment be worth in two years? We could approach this question in the same way that we have done in our previous examples.
So if we increased by 17%, this would represent 117%, and that's equivalent to 1.
17 as a decimal.
Therefore to increase by 17% twice, we could calculate 13,000 multiplied by 1.
17, multiplied by 1.
17.
And this gives us 17795.
7, leaving us with a final answer of 17,795 pounds and 70 pence.
Now, another way to look at this question is if we look at our multiplications of 1.
17.
We've multiplied by 1.
17 twice.
So we could calculate 13,000 multiplied by 1.
17 to the power of two.
And this will also equal 17795.
7.
This is a more efficient way to carry out our calculation.
Let's have a look at this example.
The population of a country is 2,700,000 and increases by 2.
3% every year.
What will the population be in three years? Well, if we take 100% and increase it by 2.
3%, this would give us 102.
3%, which is equivalent to 1.
023.
Therefore our calculation could be 2,700,000 multiplied by 1.
023, multiplied by 1.
023, and multiplied by 1.
023.
So that's the third year of a 2.
3% increase.
This will give us an answer of approximately 2,890,618.
However, again, if we look at our calculation more closely, we can find a more efficient way to carry this out.
So we could calculate 2,700,000 and we could multiply by 1.
023 to the power of three.
As this is equivalent to 1.
023 multiplied by 1.
023, multiplied by 1.
023.
And of course, this will give us the exact same answer.
Here's a question for you to try.
Pause the video to complete your task and click resume once you're finished.
And here are your answers.
So we began with 40,000 and we multiplied by 1.
15 to the power of three.
This is because we had three increases of 15%, and that led us to our answer of 60,835.
And then for the second question, we increased 7,000 by 6.
2%.
And we did this four times.
So increasing by 6.
2% will be equivalent to finding 106.
2%, which is 1.
062 as a decimal.
And then when we calculate that we get our answer of 8,904 to the nearest pound.
Here's your last question.
Pause the video to complete your task and click resume once you're finished.
And here is the solution to your final problem.
So looking at the Standard account, we can see, we get a total of 9.
75% across the five years.
And when we calculate the Advance account, we get a total of 8.
13% as the total increase.
Therefore our final answer was the Standard account as that accumulated the most amount of interest over five years.
And that brings us to the end of our lesson.
I hope you're feeling confident with repeated percentage increase.
I will hopefully see you soon.
