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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.