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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.


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.


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.


Seems reasonable enough.


Gosh, that seems quite high, but okay.

I could maybe accept that.


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.


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.



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.