What would the value of £300 become if it grew by 5% and then another 5%?

If an antique appreciates by 6% per year for 11 years, the decimal multiplier would be 1.06^11.

If I want to find the 'original' price of something that is currently in a sale and has 40%, I always need to find 100% of the amount to work out the original price.

If I start with a number, increase it by 30% and then decrease it by 30%, I get back to the original number.

The decimal multiplier to increase an amount by 6% for 5 years would be...

Repeated percentage change

﻿Hello and welcome to this two part series, this little bit here on compound appreciation and depreciation. On the growth and decay topic. I am going to ask that you go into your room that you need to in order to get away from any distractions you may have. Make sure your phone is silenced. And you can't hear it or listen to it or no notifications going off, et cetera. And that you've got a calculator and you've got your pen and paper ready to go, et cetera. So without further ado, let's take it away with Mr. Thomas' lesson. A vintage watch bought for 80 pounds increases in value by 50% every year. What is it, what is its value after two years? So been said that 50% of 80 is 40, so 80 plus 40 plus 40 is 160. Well, Zaki over here has said 50% of 80 is 40. Et cetera, et cetera. So following their working out, follow their reasoning, who do you think is right? Who do you think is wrong? Up to you. I'll give you six minutes to have a go at that. Pause the video now, have a go. Excellent, let's go through it then. So this would be correct but what we've assumed is that it's just increased by 40, a constant amount each time. So it can't be that because it increases by 50% per year. So it's going to have to be 50% of 80, that'd be the first one. So that'd be correct up until the first year. But then we're going to have to multiply that whole thing there by 1.5. So unfortunately she's wrong. What about Zaki though? Well Zaki said that 50% of that is that. 50% of 120 is 60. So this seems to have a bit more merit to it doesn't it? Right? This one here is correct because they've done 50% of 120, the cumulative total so far which is 60. So 180 is correct. You could be pedantic and say 180 pounds right? Very good. So if you'll connect there I want us to explore the idea that if you have 1000 increased by 10% each year, and I can see 10% each year, increase by 10% each year relates to that 1.1. Then each year part is that N there right? So how much would 1,000 pounds be worth in blank years time if it grew by 10% per year? Well that would be 10 years, I can see that from that alright? So that's that bit there, that 10 there circled for you. And then I can see that it's going to grow, and it's going to grow and it's going to grow. And it looks like this. In 10 years time you can see it's just over two and a half thousand pounds. It's going to be there right? So that's in 10 years time. You can see it just grows and grows and grows, that curve gets steeper and steeper. How much would three and a half thousand be worth in four years time if grew by 7.8% compound interest per year? Now compound interest is the interest upon interest. So that growing, yeah, as we get bigger and bigger, it's not just the sum itself, the principal amount, the amount we started with, it's the interest as well accumulated on top so all that happens is it gets bigger and bigger. So that would work out to be 4,726 and 54 pence. Now for you independent task today I want you to have a go at those four questions just there. You may need to know that you can have a decrease compounded as well to the power of. So think about that one. I haven't gone through that necessarily but I think you can have a go at it. So I'd like you to pause the video now and have a go at that for the next 10 minutes please. Off you go. Excellent, let's go through those answers then. So if it's 150,000 invested for 12% compound interest per year, in six years that would be 296,073 pounds and 40 pence. Give yourself a tick if you got that. Equally 1.4% would be, increase, would be 1.014 to the power of two, 'cause it's two years just there right. Can see that. A vintage wine is purchased for this amount. It's predicted to grow three percent a year so with that in mind what we can get in 19 years time is going to be 1.03 to the power of 19. So we can see that it's grown to a considerable amount. And then number four, we can see here that if it decreases by 10% per year, what's going to happen is that it's going to go down of course. So it's going to be 0.9, I'm decreasing by 10%. So for three years of course right? Really bolding this so you can see it there. So you can see that it, it works both ways. It can go down, can go that steady curve downwards, or that steady curve upwards. So for our explore today I'd like you to have a think about this. Famous mathematician has 1,000 followers on social media. How many followers do you think they will have in a year if that number increases by a mean of one percent each day? How many followers might they have if it increased by a mean of two percent per day? What percentage increase would they need to have 10, sorry 100,000 followers after one year? So pause the video now and have a go and think about how that relates to what we've just done. I will give you 10 minutes to do that, off you go. Very good, let's go through it then. So 1,000 followers on social media. You're going to have to do 1,000 multiplied by 1.01. And then what we want to know is after a year, and it's a daily thing. So we've got 365 days in a year. Now if we type that into our calculator what do we get? Well we get, 37,783.43433. So we truncate it, we round down. 'Cause we can't have .4343 of a person. So we simply say that there are going to be 3,778 followers. What about if it was a mean of two percent a day? Well that's a slightly different case because we now change our multiplier to 1.02. So 1,000 multiplied by 1.02 to the power of 365, and that would be equal 1377408.292. Truncate it so we get rid of that so it's going to be almost 1.4 million followers right? Quite a few followers there. And it's just a slight change but you can see that effect of compounding has a huge increase right? Really really big increase in those final few days. Then what percentage increase would they need to have 100,000 followers after one year? So you're going to have to play around and see what you can get to. It's going to be somewhere between one and two percent, but I'll let you play around with that and see how close you can get to exactly 100,000 followers. And that brings us to our end of our lesson. You've done an amazing job to keep up with that. It's some really powerful concepts that you've covered there. For now though make sure you smash that exit quiz and do a really good job there. For now I shall see you later. Goodbye.

Decreasing £100 by 5% for 8 years would give a final balance of...

If I deposited £500 in a bank account and left it there for 6 years at a rate of 4% compound interest, how much would I have at the end of the 6 years?

If an antique was originally bought for £55 and grew by 6.5% per year for 7 years, then the value at the end of 7 years would be £85.46 (to the nearest penny).

If 53 increased by 23% for 'n' number of years, which of the following would provide a general formula to work out how much it had grown to?

If an antique grew 6.5% a year for 7 years from the purchase price of £55, it would be worth £85.46 (to the nearest penny).

Compound appreciation and depreciation (Part I)

In this lesson, we will learn about elements of compound appreciation and depreciation.

Maths

Y9 Maths

Key Stage 3

Year 9

Compound appreciation and depreciation (Part 1)

Growth and decay

Ratio and proportion

THEME

UNIT

Percentage recap

Percentage change

Finding 100%

Compound appreciation and depreciation (Part 2)

To the power of n

Exponential growth

If the amount of flour in a bag increased by 20%, it would always mean we add 20g on to the amount.

If you decreased an amount by 60%, the decimal multiplier would be 1.60.

If I decreased the amount I paid for my car insurance by 90% to £36.50 per year, how much did I pay previously for my car insurance?

If I know something costs £2.10 in a 30% off sale, then I would calculate £2.10 = 70% and scale accordingly to get that 100% = £3 to find the original amount.

y = 9^x would cut the y-axis at the coordinate...

100% of any number is simply the number itself.

£100.00 decreases by 5% in one year, followed by an increase of 5% in the next year, and then decreases again by 2% for 8 years. What would the final amount be?

Starting with 100 bacteria, how many would there be after 1 hour if the number of bacteria increases by 20% every 12 minutes?

The decimal multiplier to increase an amount by 53% would be...

If I buy a car in a 20% off sale and it costs £30,000, how much did the car originally cost?

If y = 5^n, what is the value of y when n = -3?

In order to increase an amount by 7.5% for 3 years, I would need to multiply the amount by 1.075^3

If a bacterium increases by 1% in 2 minutes, would this form an exponential curve?

If an investment doubled every 3 years, would the growth of the investment form an exponential curve?

Lesson overview:Compound appreciation and depreciation (Part 1)

Core Content

Growth and decay: