Numbers and numerals

Axioms and arrays

Factors and multiples

Order of operations

Positive and negative numbers

Expressions, equations and inequalities

Angles

Classifying 2-D shapes

Constructing triangles and quadrilaterals

Coordinates

Area of 2-D shapes

Transforming 2-D figures

Prime factor decomposition

Conceptualising and comparing fractions

Manipulating and calculating with fractions

Ratio

Percentages

Different number systems

Sequences

Forming and solving equations

Forming and solving inequalities

Linear graphs

Accuracy and estimation

Algebra and problem solving

Ratio (8.6a)

Ratio, real life graphs, and rates of change

Direct and indirect proportion

Univariate data

Bivariate data

Famous maths problems

Angles and parallel lines

Angles in polygons

Bearings

Volume and surface area of prisms

Area review

Circles

FDP review (9.1a)

Probability

Sets and Venn Diagrams

Solving linear simultaneous equations algebraically

Solving linear simultaneous equations graphically

Angle review (9.5a)

Constructions, congruence, and loci

Pythagoras's theorem

Ratio review (9.7a)

Similarity and enlargement

Surds and trigonometry

Quadratic expressions (9.9)

Quadratic equations (9.10)

Indices and standard form

Growth and decay

Finance

Maths

Y9 Maths

Key Stage 3

Year 9

UNIT

In this lesson, we will learn about how income tax in the UK is calculated and used.

Income Tax

﻿Hello. Welcome to this online lesson on financial mathematics, which were first studying income tax for our first lesson. As always I want to make sure that you are making sure your phone is Switched Off and your apps are nice in songs and not going to disturb you that you are in a nice quiet space that you can concentrate and that you are ready to learn, Of course. My name is Mr. Thomas, I'm going to be taking you through this little series on financial Maths. So without further or do get yourself a pen and paper and a calculator and we will be on our way. So if you're try this, what I'd like you to do is these following questions, pause the video now, give yourself five to ten minutes to have a go at that Please. off you go. Excellent. So did you get these answers just here? So 0% of 10,000 of course is 0 pounds because, Well 0% of anything would just be 0. 20% of 20,000 will be 4000 pounds, 40% of 75000 pounds would be 30,000. You could divide by 10 for both of those known terms or by 2 to get to 20%, get 10% by dividing by 10 and then multiplying by 4 et cetera. You could do a bar model splitting up into ten equal parts. 1,2,3,4,5,6,7,8,9,10. So you can split a bar equal to ten parts that would work. And then seeing you need two of them or you need four of them et cetera. Same thing for this, You can split it into 20 equal parts and do the same process, times it by nine or four equal parts. and then realising is divided one of the equal parts by two and you get that. So those are the correct answers there, please mark your work now and make sure that you've done the Corrections if they are wrong. So then the sum of all those well, okay, that's interesting. So the sum of all of them, then be 0 plus 7,500 plus 4000 which would give me 11,500. Now, this is really important, the title of the lesson, right. This is an illustration of income tax rates. This one here. This is how you may think that it's done and how it's actually done. We are going to explore that a little bit further. So you hold tight for one moment, don't worry, we're going to explain that further. So for our connect today what I want us to think about is what a tax is and tax is the idea that it's compulsory amount or percentage from an individual or firm to contribute state revenue. And then income tax specifically, is a percentage based tax placed on an individual's income. So with that in mind we can say that, a tax is generally something good for society, it helps us raise revenue. Our government can spend on vital services such as the NHS and education. Anything at all. So what does it actually look like in real life? Well, this is what it does look like. So you pay 0% on the first 12,500 pounds earned, which is 0 through to 12,500 pounds Of course. Then you pay 20% of your earnings are taxed for the next 37,500 pounds. So anything between 12 and 1/2 and 50,000 pounds that you may have. 40% for the next 100,000 lets say 50,000 to 150,000. 45% thereafter, so above a 150,000 pounds. so fingers crossed, just as far that you're going to be earning as much as that you maybe wanted to be a football player or a businessman, they could be adding up in this sort of bracket up here. So really important if you do go on to do anything in your life and you are going to be earning money of course that you are aware of these income tax rates. so, how much income tax would you pay then, if you earned twenty seven and a half thousand pounds per year. Where you pay 0% on that first 12 and a 1/2 thousand pounds you earned. You then pay 20% on the following 14 and a 1/2 thousand, because 27,000 pounds subtract 12 and a 1/2 thousand pounds is equal to 14 and a 1/2 thousand. So actually it becomes a really simple problem at this point. We do the sum of 0% of 12 and a 1/2 thousand pounds, which of course is zero pounds and 20% of 14 and a 1/2 thousand pounds. Therefore, in reality you pay 2,900 pounds per year in income tax as a result. So it's what we call on marginal tax. It depends on how much extra, that one extra pound that you earn that could be taxed that one extra pound at 45% or it could be taxed at 0% depending on where you are and which bracket you're in. So let's have a go of this from how much income taxes would you pay, if you earned 24,000 pounds per year? You can have a go at this yourself if you want to but pause the video now, or I'll go on. So you pay 0% on the first 12 and a 1/2 thousand pounds. From? We got that. We saw in the previous example. we then do 20% of the following 37 and a 1/2 thousand pounds. You then do 40% on the following 24,000 pounds, because the idea here is 74,000 subtract 50,000, We've got to that point there're at next bracket, would be 24,000 pound that will be taxed at 40%. So now becomes a simpler problem. The sums are the percent of 12 and a 1/2 thousand pounds, 20% of 37 and a 1/2 thousand pounds and of course 40% of 24,000 pounds. So when you do all those sums and you add more together you get 17,100 pounds per year in income tax. Quite a lot to be paid. But of course it all pays those vital services that we know and we love around our country. So what I'd like you to do now for your independent task is I'd like you to have a go at working out, how much income tax you pay with the specific amounts there. I've got the reminder there just to help you. Pause the video now. I'll give you 12 minutes to do that please. off you go. Excellent. So the answers are as follows then. So for number one, if you were to do that one there, you pay of course zero pounds in income tax, because you haven't earned enough to be taxed. Right? number two, you do 20% Of 15,000, the difference between 15 thousand, and 12 and a 1/2 thousand would be 2500. So we need to 20% of 2500 and that would of course be 500 pounds. Number three, 24 and a 1/2 thousand pounds. Well that one there, would be the difference between twenty four thousand five hundred and twelve and a half thousand so we'd have to do 20% of this one here, would be 12,000 pounds. So with that case, we do 12% to 20% of 12,000 pounds, which of course would give us 2,400 pounds. Number 4, what we do for that one there, we will do, 20% of the ... The one we do is 0% first of all of the 12 and a 1/2 thousand. We then know it's going to take us to the next brackets. so it's 37 and a 1/2 thousand pounds. So 20% Of 37 and a 1/2 thousand pounds adds, but will then be up to 28,900. So if 40% Of 28,900 pounds, so in that one there, we get our first answer as being, well our first answer that be? it would be 7,500, good. And then the next one, we'd add 40% of 28,900. That'll give us an 11,560. So if we add those two together, of course we get 19,060. Very good If you got that. Now if you're doing a 190,000 per year, fingers crossed, you will be adding such a high amount at some point. I'm going to do that just over here. Now number five, we'll 0% of 12 and a 1/2 thousand. Where we know that. We can also just use the answer from over here, the 20% of 37 and a 1/2 thousand. So we not going to have to do 7,500, because that refers to this income bracket here, this 20%. And then we're going to have to add on 40% of a 100,000. Right? Because we go up to that initial limit there. So that's going to be, what would that be? 40% of 100,000. That's quite nice easy one, 40,000 pounds, isn't it? And then we can add on 45%,thereafter 45% of 40,000. So 45% of 40,000 would give me 18,000 Pounds. So when I add those all together, what I get is of course, what do I get If I add these all together? Tell me now, nice and loud 65,500 pounds. very good. And then the final one. I'll do that up here a little bit messy in terms of not reading out loud. You get the idea. So million pounds per year. Well, we can steal the idea that we had this bracket here, this 20% and then the 40% maxed out. right? We have 7,500. Plus 40,000. And then we're going to add on 45% worth of 850,000 pounds. Do you see that We're doing a million subtract a 150,000 pounds there? So what we get is, what do we get if we do that? 382,500 pounds. when we add that all together what we get of course is, what do we get if we add that all together? Come on. All most there, 430,000 pounds. Now, actually you're thinking that's probably really high figure. I haven't even take into account some tax allowances you can have at that high level and you actually saw some more punitive measures in some ways. Actually that you get that tax-free allowances to deduct it at certain point, but I've kept the example simple for now. So with that in mind we can go on. So if you were Explore task what I'd like you to think about is if you're the Chancellor of the Exchequer, someone who ultimately decides on whether tax rates change in the country, Would you increase or would you decrease income tax? If you increased income tax for every band, would this lead to lots of extra money for the Government? So much on revenue. Asking yourself where would actually get more money if we increase taxes. Why might it not? and would it be best to have a flat rate system where everyone pays the same rate regardless of earnings? So I want you to pause the video, have a think about those questions for the next 15 minutes, please. Off you go. Very good. Let's go through it then. I'll provide some support if you do need it. So if you were the Chancellor of the Exchequer, would you increase or decrease income tax? Well, this is a really difficult question and there's no right or wrong answer. If you mean increase income tax you get more money coming in. So you get more government revenue coming in, income Revenue, tax revenue to your government coffers. So you can spend more money in the economy. However, of course that means that people like yourself and me and everyone else we don't have as much money to spend. If we are in a job and we're not getting as much money because of all this going out for tax. So in that sense, it's really difficult to get the firm balance of what's a good tax rate was and what's a negative tax rate in that sense? So there is no right or wrong answer. So if you're increasing income tax fore every bound, why would this lead to loads of extra revenue for the government? Well, that we just said. If you have an income tax rate of say like 90% for every single bracket, then of course you get lots and lots of money, but the problem being, if you were earning so much money, you could just potentially move abroad, can you? You could transfer your wealth over, you can transfer your job over. Particular the moment of what's going on, we can see more and more people are working from home. They can work at home from abroad, they can work their own business, they can transfer the businesses abroad Et cetera. So it may not be the best idea necessarily to Increase the income tax for every bands possible. Would it be best to have a flat rate system? Well again, that's up for interpretation, that's for you to decide. Some countries have pursued that. well they've said, "everyone pays 20% regardless their earnings." Some people say that might be unfair on those on the lower bracket and that its harder hits them, but then again for the more wealthy, it's fair in the sense that everyone is paying the same, everyone pays their own dues to the Society. So again is very much up for discussion and for you to research as a whole. So with that in mind, that now brings us to the end of our lesson. You've learned lot in this, lots and lots of Applied stuff in terms of Mathematics and percentages with Finance et cetera. So done a really good job to be able to keep up with that. It was quite a tricky topic that is actually very poorly understood by a lot of adults and indeed people across the country. So with that in mind, please take that exit quiz that you can smash it and prove to me how much you've learned. So without further ado, I will be saying goodbye and wish you a good day and Just stay safe.

In this lesson, we will learn about the general principles of mortgages and mortgage loan repayment.

Mortgages

﻿Hello and welcome to this online lesson on Financial Mathematics, Mortgages this time. It's the second lesson we're doing. I just want you to make sure you're in that quiet space, you're able to relax and you're able to concentrate as much as possible, that your app notifications are turned off, and they are not going to disturb you in any way, shape or form, and that you're able to concentrate on the maths because there is a lot to take in in this one and we need to make sure we're concentrating a lot. So without further ado, let's take it away with Mr Thomas' lesson. Now, for your 'try this' today, what I'd like you to do, so I'd like you to have a think about the questions that are posed there. If I borrow £150,000 at an interest rate of 3% a year, how much do I owe at the end of... And I want you to assume that compound interest occurs, and you do not repay any amount during the time specified. So, pause the video now and have a go at that task. Very good, so these are the answers that you should have, remember we have this decimal multiplier because that is increasing, so that means increasing by 3% per year because we've got it to the power of one. Do you see that? It's the power of two there, three there because it's three years etc. And when we get this, we're rounding to the nearest penny, when we get to this point. So we see that £150,000 has well over doubled in that period of time from 30 years there. So it's really really important you're able to control the amount that you borrow because otherwise it could spiral out of control if it does get to the point of 30 years time. 30 years time, goodness me! So really really good stuff there if you've managed to do that. So for our 'connect' today, what I think us to think about is a few definitions first of all. Now, mortgages. What are they? Well, they're a debt that must be repaid, with interest, as a result of purchasing a house. And maybe, like the house I'm sat in at the moment, you may want to be able to purchase something like this. Right? It's really really important at some point in your life, I'd say at least, to be able to own something that is yours, in terms of maybe a flat, a house etc, some people decide to rent all their lives and that's perfectly fine as well, but you generally speaking want your own space of some sort right? You want ownership of your own space. So you'll take on a mortgage when that happens, and you're not going to be able to afford say, or the typical person won't necessarily be able to afford £300,000 for a house, they're going to have to borrow some of that of course. But they'll pay it back over the course of their life, to the bank. And what happens is, there is compound interest on there, so it's the interest that accrues upon the initial amount borrowed or saved, and the interest as time goes on. So you get interest upon interest, sounds horrible and it is a little bit because it can lead to really really big problems if you're not controlling it enough. So the typical term of a mortgage is between 25 to 35 years that you repay it, and remember, like I was saying a moment ago, you can have debt spiralling out of control thankfully mortgages, they spiral less out of control because the interest is quite low on them. But with this, with just 3% interest, you'd need to pay over £360,000 back on that £150,000 borrowed. So it's really important you're able to be aware of that, that you'll be paying back if you take on a mortgage of, say, £150,000 for 30 years, then you would need to pay back well over double that just with 3% interest so be really aware of that. And, of course, you gradually pay it off through those years. So I've assumed you haven't necessarily paid it off throughout all of those time periods, because it gets quite complicated when you do that. But we're simplifying the calculations here. So, what I want us to now assume is that you've bought a house and you've got a mortgage of £120,000, how much would you pay, assuming compounding interest and no repayments, over the course of 25 years if the interest rate was 15% first of all. Well, in order to work that out, I'd do £120,000 multiplied by 1.15 to the power of 25. Now, if we get our calculator out now, and we have a go at that, what's that going to be? Well that's going to be a pretty hideous sum of money, a pretty big sum of money. That is going to be £3950274.31 to the nearest penny. So when I separate all that together, that is going to give us £3.95 million, right, so that's a heck of a lot of money to have to repay. What about this with 10%? Well, 120,000 again, times by 1.10 to the power of 25. And that's going to be equal to, if I do that, that'll be equal to £1300164.71 to the nearest penny. So that there, if I separate it, is going to be just over 1.3 million, so again a heck of a lot, goodness me, it really depends on this interest doesn't it? Almost 4 million here, and then that decreases to 1.3 million here. What about 5% this time? Right, what about 5%? Well that one there, if we did that, we'd do 120,000, of course, multiplied by 1.05 and that would give us £406362.59. So £406,000 if I Was trying to round that down. So again, that's a little bit more manageable, isn't it? We can maybe understand that. What about 2% then? What about 2%? Well, 2% would result in £120,000 multiplied by 1.02 to the power of 25, and that would be equal to £196,872.72 to the nearest penny. So, we can see that's a lot more manageable over 25 years, repaying that amount there. So it really does depend on your interest rate, I think you can see there. So for your independent task, what I'd like for you to do, is, I would like you to have a go at those questions there. Pause the video now, I'm going to give you, how long should I give you? I reckon you can do this in 12 minutes, so pause the video now, and have a go at that task. Off you go. Very good. Let's go through it then. So, what I'd like you to do is to mark your work right or wrong, this one of course, you're going to have £150,000 with 2% interest over 35 years, that would be 150,000 multiplied by 1.02 to the power of 35. What about this one here? This one here, with 2% interest over 35 years for £300,000, well, what we're doing is just changing the number there, it'll be 300,000 times by 1.02 to the power of 35. And that would give us this to the nearest penny. Notice there is a little relationship between those ones there, right? Number three, what about this one? £950,000, so you're making loads of money and you're able to borrow loads of money as a result, 5.4% interest, well, that would be 950,000 times by 1.054 to the power of 25 years, right? So that would give you almost 3.5 million, goodness me, a really high figure there. And then the final one, is going to just be shy of 1.8 million, that'd be 641000 with an interest rate, of, what would it be? Interest rate of 1.0415 to the power of 25. Right? Very good. So we can see that, it really does evolve over time, these calculations, it's so so important you're able to see that compounding effect going up and up and up, exponential curve. So for your explore, what I'd like you to think about, is the following: that most interest rates at the moment, at least, in July 2020, they're around 3% at the moment. If you ran a bank, what interest rate would you charge and why? If you charge a very high rate, would it be ethical? Would you get many people inquiring about getting a mortgage? Then if you had a very low rate, for that first question, would you make enough profit? How have the prices decreased? And then, second, as a result of everything we have learnt so far, how complex is it to know how much you are paying for a mortgage, let alone run a bank? Right. Such a complex operation, that's your clue there. So, pause the video now, I want you to think about that for 10 minutes please. Off you go. Okay, brilliant, let's go through it then. So, if you ran a bank, what interest rate would you charge and why? I'm going to leave that up to you. If you charge a very high interest rate, you probably want to make loads of money. If you charge a very low interest rate, you just want to help people out. If you charge very high interest rate, would it be ethical? Well, there's arguments here for and against, and we're going to explore that later on in the series. But, I don't think it would be necessarily ethical because you have lots of your customers getting into, what we call, debt spirals and debt mountains, and they're really crippled by this idea of debt, when it comes to repaying it, they're not going to really be able to pay it, which is a big concern. Would you get many people inquiring about a mortgage? Well you probably wouldn't get many people at all because you could go to another bank, at a lower interest rate. So really think about that one, because it may not be the best idea. If you had a very low interest rate, would you make enough profit? Well, you'd have to borrow, ultimately, from another lender, in the UK it's called the Bank of England. That's quite a complicated topic. But, essentially, you can borrow for a very low amount at the moment, as a bank, 0.1%. But you need to take into account all those other costs that you may have as a bank in terms of employing your staff, etc. So, such a complex issue. Then, what if house prices decrease, well, your homeowner could be left with very little if they really did decrease which is unlikely, but it's still a possibility to consider. As a result of everything we've learnt, well, we can clearly see its very very difficult to realise how much we need to pay, ultimately, through those time periods. I've really simplified the mortgage process here, there is a little bit more to it, quite a lot more to it to be honest but I've streamlined it for your benefit and you can see how much you would have to repay if you separate that over monthly payments you could even see how much you repay monthly. And that gets us onto more complex topics that I didn't want to cover in this video. And we can see its very difficult as a result to know how to run our bank. So, that brings us to the end of our lesson today. I just want to say a big congratulations, really really good stuff if you're able to keep up with that, because that is a really complex topic that, if I'm being honest, not many adults fully, fully appreciate. It's really important that you understand that early on, because when you go to get a mortgage, and you see what interest rate you're being charged that is what could be with you for the next 20, 30, maybe even 35 years. So really important you're able to understand that. Remember to smash that exit quiz, so you can prove how much you've learnt to me and everyone else. For now though, I will be seeing you, and take care. Bye bye.

In this lesson, we will learn how savings grow over time. We will investigate how to calculate the amount of time it would take to save a given amount with regular small deposits, and the concepts of simple and compound interest.

Savings

﻿Hello and welcome to this online lesson on financial mathematics, our third lesson in the series on savings, as always, I'd like to make sure that you are in a safe area and that you are distraction-free and that you are making sure that your phone is on silent or that the app notification is not a ping. So you can make sure that you're going to focus entirely on the maths cause there's lots of complicated things that are going to make very little sense unless you're concentrating very, very carefully so make sure you are concentrating please. Make sure as well, you've got a calculator to hand and you've got some pen and paper, so you can write some ideas and notes on. Without further ado, let's take it away with Mr. Thomas's lesson. So if you'll try this, I'd like you to have a go with this. If you managed to save 25 pounds a month, how long would it be before you had a thousand pounds, 2000 pounds, 1,975 pounds and 27,525 pounds? Pause the video now and have a go at that task, please. Excellent, did you get these answers here? So this one here would be 40 months cause you divide them so thousand divided by 25 to see how many months it would be mark it right or wrong please, it'd be 40 months, which is three years, four months. 80 months because it's actually just double the previous answer if you see the relationship there. The following one is going to be simply be one last month in the previous one, because if you notice there's 25 months there, or you could dividing it 79, that would work as well. And this one here would take a heck of a long time, take 91 years, nine months, a long time there. If you've got that, very well done. Let's move on. So for you're connect today, I want to recap the idea of compound interest, which we've covered before, but also simple interest. Now simply interest is the idea that interest is included upon the adjust initial amount. So it's really important you understand that because that is quite basic, that's not too tricky to work out and we'll see how we do that in a moment. But compound interest is the absolute one, which is very, very interesting and gets bigger over time. And it's the idea that when you get interest it accrues upon the initial amount borrowed or saved and the interest as time goes on. So it forms like an exponential curve as we've seen before. Now let's put it into context then. So if I save 10,000 pounds in the Oak National Bank at 3%, how much interest would I have gained after five years assuming simple interest and five years assuming compound interest? Where if I were to assume simple interest here, what I do is be working out 3% of 10,000 pounds. So I do 0.03 times by 10,000, nothing too tricky there that gives me three pounds. Times it by five of course and that gives me 1,500 pounds. So I've gained 1,500 pounds by saving at the Oak National Bank, seems pretty good. What about compound interest though? Well, that one there, I'm going to do 1.03 times by 10,000 pounds. Cause I've got 10,000 pounds saved and that would be equal to, have I made a mistake there? What have I done? It should be to the power of five, shouldn't it? My cough gain to me. So 1.03, to the power of five times by 10,000. And that gives me if I put that into my calculator, what does that give me? Are you going to beat me to it? What's it going to be? It sounds like you are. I mean, quite slows down my calculator. What's it going to be? It's going to be 11,592 pounds, 74. Now that's not how much interest I've gained though. I need to subtract the initial amount 10,000 from that. So that would give me if I do that 1,592 pounds, 74. Now you're probably thinking in your mind, well, that's not a huge difference, but actually what we've noticed is is 92 pounds 74 more and that can add up over time. Let's try it now with 32 years, we're going to have to do 0.03 again times by 10,000. So that gives us 300 pounds and then multiplied of course, by what would it be? 32, right? So if I do that, what do I get more 32 multiplied by 300. You probably even quicker than I am be 9,600 pounds. And if we were to do this for the compound interest example, what would be 1.03 to the power of 32? And that would be most applied by 10,000 and the answer would get would be, what would it be? Again, you're probably even quicker than I am. You're going to beat me to it, I've got it. It's going to be 25,750 pounds and 83 pens to the nearest pens. So I can then subtract the initial amount as we did before. And what I get is what I get this time, subtract some 10,000 from that. I think I'll be here this time. So that's going to be 15,750 pounds and 83 pens. Now we can see there's a bigger difference here, right? 9,600 versus 15,750 pounds and 83 P. So there's a lot bigger difference. Let's push that even further and go for 110 and a half years that would be really interesting to do so that one there, excuse the pun. Of course, interesting. Anyway, 0.03 multiplied by 10,000, we get that age old answer of what would that be? 300 pounds, right? We then need to multiply that by 110.5. We've assumed you were going to get half year there as well. So 110.5 multiplied by 300 gives me 33,150 pounds. Now I think you can probably tell it's going to be a very big difference between these two numbers. So if we do it, so we get 1.03, to the power of 110.5 and then multiply that by 10,000, we're going to get, what we're going to get? You probably even done it before me, cause I've laboured myself really, really painstakingly writing on my why or my whiteboard here, what would it be? Times it by 10,000, it would be, that's a big number, it's going to be 262,127 pounds and 95 pens. So you can see and then of course, well that's not our final answer is it? It is not a final answer. What would be our final answer then? I'd have to subtract that 10,000 wouldn't I? And if I do that, I get 252,127 pounds and 95 pens, 10 narrows penny. So we can see that there is a big difference between those and that shows you the effects of compound interest over time, it could work nicely with savings, but it can be deadly if you have it with loans and you can get out of control in terms of debt mountain. So for you're independent tasks today, I want you to assume you've said 25,000 pounds in the Oak National Bank at 3%. I want you to work out how much interest would you have gained after these time periods here, assuming various compound or simple interest. So pause the video now and have a go for the next 10 minutes please, off you go. Very good, let's go through the answers then. So if you did a three years, assuming simple interest, that'd be 750 pounds for the first year, times by three, 2,250 pounds, please mark it right or wrong. The next one you'd less of course, the two 25,000 pounds that you'd have there. So you'd work it out and you get 2,318 pounds and 18 pens. So again, not a huge difference everyday over three years, you're going to see what's happening now, 27 years, it's going to be 20,250 pounds for the simple interest. That should be fairly intuitive. But this one here you can see there is pretty big gap now, is it almost 10,000 pound difference there. And then of course, for 120 years, you can see the gap is colossal. You can see that that's almost 10 times the amount there, 90,000 versus 842,000. So you mark them right or wrong please, Now for your explore task today, what I'd like you to think about is the fact that most interest rates for savings accounts are about 1% at the moment as of July, 2020, when I'm doing this video. Now, if you've run a bank, would you prefer to give your customers compound or simple interest on their savings, why? If you're a customer of a bank, would you prefer to have compound or simple interest on your savings and why? I'm going to give you five minutes to have a think about that. So pause the video now and have a go at that task please. Excellent, let's go through it then, I'll provide some support if you are struggling. So if you're a bank, what you probably say is if you're, if you want to minimise the amount of going out, you don't want to give as much money away. So you're going to want to give yourself, you want to give your customers simple interest because that minimises the amount paid out, which therefore increases your profit. You want to make as much profit as possible. You could be returning it to shareholders. You could be giving it to your staff in the form of bonuses. You could be giving it away to the community. It could be anything, but you want as much profit as possible. That's generally the accepted idea of business that you want to make as much profit as possible. So if you're a customer of your bank, would you want simple or compound? Well you'd want compound of course, cause you want to maximise. And we've seen how savings increase over time. And that maximises is the opposite. You want to maximise the amount paid out, which therefore of course increases your savings. So you can see this conflict between both the bank and the customer, they're always seeking customers, always seeking myself, I'm always seeking the best rate when I look to save, but equally the bank doesn't want to give as much away. So they want to reduce their rate as much as possible, but it's all dependent on demand. If they're not getting enough customers, they don't have to raise it their interest rate in order to get customers, to save with them. So it's a very fine balance. And that brings us to the end of the episode for today's lesson that I've done. So you can see how amazing it can be having compound interest attached to savings over time. And also you can probably see the other angle as well. How has a real big conflict, whether a bank should be paying simple or compound interest or whether you want a compound or simple interest, you now understand those intricacies and those small little nuances in the system and you're clued up financially, which is brilliant. So make sure you take that exit quiz and you smash it out of the park and do as best you can. For now, I hope to see you in the next episodes, the final one that we're going to on payday loans, take care and see you later, bye bye.

In this lesson, we will learn about how payday loans work. We will investigate the risks involved in high interest loans and calculate regular repayment plans including comparing total repayment costs to original loan amounts.

Payday Loans

﻿Hello, and welcome to another lesson on Financial Mathematics. Our last lesson in this series on Payday Loans. It's really important that you've got those app notifications turned off and you're ready to learn because you're not being distracted by anything, that you've got that quiet space that you can focus in as well. And you've got pen and some paper, you can write some notes on and your calculator as well. Really important 'cause you can do loads and loads of things involving calculators and all sorts of things there. So without further ado, let me take it away, Mr. Thomas' lesson. So if you borrowed a hundred pounds for three years, how much would you have to repay under those terms of compound interest just there? So pause the video now and have a go at it for eight minutes, please. Off you go. Excellent. These are the answers, you should have got those. Now, if you've been listening for the past few series, the episodes and series, you should know those three there. The one that may complicate things a little bit though, is this 16. Now, if we go back to this first one and I explained what the multiplier is here, it's one, plus the interest rate 0.05, but that's being converted into a decimal, which of course gives me 1.05. Now I've got to use this idea of the one to begin with. And I've got to say, well, one plus 15.00 because I've converted that 1500 there, 1,500, into a decimal. So that gives me 16. So just be very, very careful of that one there. Same principle applies for the 59 here. It's one plus 58.00, which gives you 59. So you may have got some answers that are close, but not quite. Now, the reason why I've chosen these examples is because they're actually really illustrative of real life interest rates. And you're probably thinking, how could I borrow a hundred pounds and it evolve? Well, to 115 pounds over three years. I can understand that. Yeah. Seems reasonable enough. 20%. Gosh, that seems quite high, but okay. I could maybe accept that. 40%. You're thinking, wow, that is a lot. I don't think that's worth it. You're probably thinking at 1500%, gosh, that really is not worth it whatsoever. That a hundred pounds is evolved to well over 400,000 pounds. That's pretty scary. And then 5800% is evolved to 20.5 million. Are you having a laugh? That's insane. How is that even possible? Well, that's what we're going to explore today because the 5% here is actually what the, what the average sort of bank loan, roughly speaking a bank loan would be charging at the moment as of July, 2020, of course. With 20% compound interest, that is, that's a credit card. That's like a, a decent credit card. A decent, reputable sort of credit card, yeah? The next one would be like, what I'm going to call, like a bad credit card. So one that charges quite high interest. It's one of the worst examples of a credit card. 1500% is a not so nice, like a bad, a bad payday loan. And we'll explore what that is in just a moment. And then what I'm going to call the worst type. This is the worst payday loan, approximately, that I've ever seen, when I've been investigating finance or when I've been doing maths related things. So it really gives you an idea and it's scary how compound interest works and how powerful it can be, both in your interest when it comes to savings, but also in terms of getting a loan. So that's what we're going to explore today. Four and five and seeing how they grow over time and what they're all about. So a payday loan is a small amount of money, usually borrowed for a short period of time, That is typically paid back when someone receives their next form of income. They often have very high levels of interest attached to them. So it's a very, very short period of time that we're focusing on perhaps, maybe a week, two weeks or a month tops. And then it goes out to be a huge, huge interest during that time. It's very short term, very high interest. The levels of interest, like I said, can be in excess of 500%. So a bad payday loan, as I said, it would be about 1500%. And the absolute worst that I've seen is around 5800%. So I want to do some more calculations to analyse those figures a little bit further. So what if the amount you need to repay, if a company offered a loan of 500% and you want to borrow 120 pounds for 15 years, six years, two years, four months and five weeks? Well, 15 years, what we'd have to do, what would we have to do for that one? We'd start off with what we call the principal, the starting amount, 120 pounds. So 120 times by, well that 500% interest, we need to do 5.00 don't we? And we need to add one to it, which is going to give us six. So we have to times it by six to the power of 15, and that would give us of course, what would that give us? That would give us a number that looks like this. 5.642219815 times 10 to the power of 13. That's probably what's appeared onto your calculator and you can't do much with that. So if you can run back to standard form, what that will give you is 5,642,219,815. So what I can do is multiply it by, that'd be by one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13. So that's times ten to power of 13 there. So what I get when I do that is a number that looks pretty hideous if I'm honest. So that gives us the thousands. That is millions. That is billions, and this is trillions. So 56 trillion pounds. Now that is pretty interesting, isn't it? 56 trillion. Let me just write that, 56 trillion. Now to give you an idea, the most valuable company in the world was valued around, it's up for debate, but around $5 trillion. And that's in dollars, not pounds and pounds are more valuable. So quite ridiculously, you get actually probably the GDP of many, many countries combined, perhaps even the world. I'm not entirely sure, don't quote me on that one. But it's a heck of a big number. It's mindbogglingly big. Have a look at it on any sort of website that compares numbers, cause that's a huge number. Six years. What about that one? 120 pounds would have to be multiplied by six to the power of six. And that would give you, if you check out your calculator, what would that give us? 120 times six to the power of six. That would give us 5,598,720 put in those commas, okay. So it's got us five point, almost 5.6 million pounds there, not quite so bad, but only 120 pounds we borrow to begin with. So that's quite scary still. What about two years then? We're going to have to do 120 pounds multiplied by six to the power of two. So that will give us. Six to the power of two you can probably work out as being 36, but either way that would be 4,320. Now six months for that one there, you're going to have to do 120 times by six to the power of a half, because we're doing it for half a year, six months is half a year and this is an annual interest I've assumed. So that is going to be, of course, what would that be? That would be 293 and 94, 93 pounds, right? And 94 pence to nearest penny. To the nearest penny. And what about two weeks then? Well, that's going to be 120 pounds multiplied by six to the power of three over 52 because there's 52 weeks in a year. So what I can do there, is I then get 133 pounds and zero, zero seven, so it's seven pence to the nearest penny. Now it's really important to be aware of this, that the most typical way that most people finance it is through five. And if you borrow 120 pounds for those two weeks, then paying back 133 pounds, doesn't seem so bad to get you out of some trouble. It doesn't seem bad. It's not actually a really terrible method way of financing. So it's just being aware that if you can pay it back in two weeks, fine paying an extra 13 pounds or so, isn't actually too bad, right? And I agree, to a certain extent they do have their value if you've got no other options. But it should be used as a very, very last resort. So what I'd like you to do for your independent task then is to have a go at calculating interest on these amounts of timeframes here with 150 pounds. So pause the video now and have a go at that task for the next 12 minutes, please. Off you go. Okay. Excellent. These were the answers here. Now, if you're confused about any of these answers, make sure you look back in the video just to make sure that you've fully understood this idea of why it's 7.5 being the 6.5, cause you've converted the 650% into 6.50 because you want to get into decimal plus that one, yeah. The multiplier to increase it, of course. So please be aware of that one there. So you can see it evolves really, really drastically over time. And of course you get charged very, very high levels of interest. So again, having seen the connect, that shouldn't have been any surprise, I've just changed the numbers there. Now, for your explore task today, what I want you to consider, if you run a bank, would you offer bank loans, credit cards and payday loans? Why would you choose to offer these financial products? Why would you choose to offer certain ones? What profile of customers would typically pursue those financial products? So what sort of people would you have getting bank loans, credit cards, maybe even businesses, pay day loans, that sort of thing. And then second, would you borrow, you personally, would you borrow using a bank loan, credit card or payday loan? Why would you borrow with that method of financing? And what could it be dependent on? So look at your financial circumstances. Why, why would you prefer having a bank loan over a payday loan? Why, why might you go actually for a payday loan versus a bank loan? So pause that video now and have a go at that for 10 minutes to really think about it. I'll be available in next slide for any help that you may need or to go through the answer for that. Off you go. Okay, excellent. Let's go through it then. So if you run a bank, well, again, this is up for interpretation, but if you run a bank, you probably would offer bank loans and you'd offer credit cards. Payday loans are usually done with specific companies that specialise in payday loans and some have gone bankrupt in recent times or have actually been shut down. So why would you choose to offer those? Well, you'd want to offer a bank loan because generally people, the profile of the person that would go for that or business that would go for that, generally secure business, right? They've got good financing. The bank is, is happy enough to lend them the money because they know it will be repaid. So they'll give, they'll give a good rate of interest. They'll give that 5% interest. It isn't really that bad at all. A credit card though, usually get sort of people like myself and you know, anyone else really in society, that's got to, myself being a teacher, quite a stable job, right? A credit card is really useful for say a monthly spending habit that you may have, and you don't have just the necessary funds right now to use it. They typically have a limit of maybe about two to 3000 pounds, sometimes stretching up to a maximum of around 10,000 pounds. You can use them as sort of again, a short term financing method, but it's important to know you can get rejected from them. So credit cards, generally, again, they have quite, you know, quite reputable, but not so secure because for loans, this is getting quite complicated now, but they take what we call collateral. So it takes some sort of insurance. They may have to, you may have to put your car on the line for example. If you don't pay your loan back, they may take your car as security. So they may take it to repay some of that loan back. Now a payday loan though is really bad. So it's not secure at all, yeah. It can go wildly out control. Anyone can get it. And that's the really, really desperate, you know, people of society that really do need that financing quick to pay back something that they may have, they may have gotten into debt about. It needs to be repaid right now and they can't get a bank loan or a credit card. So why would you borrow using that? We've kind of just been through that. You use a bank loan if you're secure and you've got some assets or, you know, you've got a house, you've got a car you could put it on the line just in case you didn't pay back. A credit card would just be like normal day to day financing. And then a payday loan would be if we're really, really needing that money right now. And we haven't got that paycheck to hand, and we've been rejected from credit cards and bank loans in the past. So it depends on what we call a credit score as well, how much we can, sort of our financial footprint, how, how well we've done in the past with paying back loans. So that brings us to the end of our series on financial maths. I hope you've had a really, really good time learning about this and there's some really, really important stuff that's applied to the real world here. So I'm really happy if you're able to keep up with that. Excellent job indeed. Make sure you are looking out for those financial products in the future. And you're saving lots and getting the highest interest rate and of course paying the lowest possible interest rate on any loans that you may get. Make sure you are sharing your work as well with the app, Oak National hashtag and all that on Twitter and that you get your parents or carers permission in order for them to post what you may have done. Now for now, I shall be seeing you later, but I hope to see you at some other point through your studies. Take care for now. Bye bye.

If a person earned £30,000, they would pay no income tax.

In the UK (as of July 2020), you can earn £12,500 and pay no income tax.

If an individual earned £35,000 a year, how much income tax would they pay?

A mortgage is a debt that must be repaid, with interest, as a result of purchasing a house.

If I borrowed £350,000 in the form of a mortgage at a rate of 3.2% per year interest for 20 years, how much would I pay back at the end? (Assume compound interest, no payments made until the end and the answer is rounded to the nearest pound).

Which would cost more? A £200,000 mortgage that had a rate of 0.5% for 35 years or a £120,000 mortgage that had a rate of 3% for 25 years?

Simple interest is the interest that accrues upon the initial amount borrowed (or saved), and the interest, as times goes on.

If I saved £5,000 with Oak National Bank at a compound interest rate of 7% for 9 years, how much would I have, rounded to the nearest penny, at the end of the 9 years?

A payday loan is defined as a small amount of money usually borrowed for a short period of time that is typically paid back when someone receives their next form of income. They often have very high levels of interest attached to them.

If you borrowed £100 at 4% compound interest for 5 years, assuming no repayments, how much would you owe at the end of the term? Round to the nearest penny.

If you borrowed £125 at an interest rate of 1,800% for 7 weeks, assuming no repayments, how much would you owe at the end of the term? Round to the nearest penny.

A payday loan is a cheaper option for finance than a credit card.

Unit Overview: Finance

Lessons:

Income Tax

Mortgages

Savings

Payday Loans