Lesson video

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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.


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.


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.