Hi, I'm Mrs. Wheelhouse, and welcome to today's lesson, which is from our unit of lessons on financial maths education.

I'm really looking forward to exploring some of the ways that we use maths in order to help out with our personal finances.

So let's get started.

By the end of today's lesson, you'll be able to describe the relationship between risk and reward in different financial contexts.

So we're gonna be using the following words today, and you're very welcome to pause the video now if you'd like, so you can have a read through some of these key terms and their definitions.

Our lesson is broken into two parts today, and we're gonna begin with risks and rewards with saving or investing.

If you receive some money which you do not wish to spend at that time, you may choose to invest it instead.

Investing is where you put money into something, with an expectation that you'll receive back more money in return.

There are different ways you can invest money.

Some investments provide greater rewards than others, and this means you receive more money for your investment.

However, some investments have greater risks than others.

For example, the amount of money you receive could be less predictable, or there could be a chance that you'd lose money.

Money can be invested into a savings account.

Banks provide customers with interest on the money that they leave in their savings accounts.

So for example, Sofia receives 100 pounds in birthday money.

She places it into a savings account that pays 3% interest per annum.

After a year, she withdraws her birthday money along with its interest.

How much money did she withdraw? Well, the interest earned was 3% of 100 pounds, which means she earned 3 pounds in interest.

This means she withdrew 103 pounds.

Now, of course, she could just increase the 100 pounds by 3%, and that will tell you that she withdrew 103 pounds.

Now, money may also be invested in other ways.

Lucas wants to start his own small business baking and selling cakes.

The initial start-up cost, ingredients, et cetera, would be 500 pounds, but Lucas only has 400 pounds.

He invites Sofia to invest 100 pounds into his business for a share in the profits.

So what would be Sofia's share of the profits? What do you think would be fair? Pause and have a quick discussion now.

Welcome back.

Well, if she's investing 100 pounds out of the 500 in total that's needed, then that's a fifth of the money, so 20% would seem fair.

Lucas spends the 500 pounds to bake a large batch of cakes.

He manages to sell all of the cakes for 550 pounds in total.

How much profit was made from the sale? That's right, 50 pounds.

Sofia receives back her 100 pound investment, plus a 20% share of the profits.

So how much money does she receive? Well, 20% of 50 pounds is 10 pounds.

So that means what she receives is 110 pounds.

You could of course have said, well, she receives 20% of the total that was made, or 20% of 550 pounds is, again, 110 pounds.

Let's consider these two scenarios.

Scenario one is a savings account.

So Sofia invests 100 pounds into a savings account with 3% interest.

She earned 3 pound from the interest, so at the end she had 103 pounds.

Now let's consider the cake business.

Well, she invested 100 pounds in Lucas's cake business and received 20% share of the profits.

This meant that at the end she had 110 pounds.

So which investment provided the greatest reward? And which investment had the greatest risk? What do you think? Pause the video and discuss this now.

Welcome back.

Well, the cake business clearly gave the best reward.

She made 110 versus 103.

However, it also had the greatest risk.

What if Lucas hadn't been able to sell all the cakes? Hmm.

So savings accounts provide relatively low amounts of reward for the money invested in them, often with interest rates under 5%.

However, savings accounts are generally safe places to invest money.

Interest rates tend to remain similar each year, so it can be easy to predict how much money you will have at the end of the investment.

In this scenario, Sofia could be confident she'd receive back her full 100 pound investment plus 3 pounds interest.

Now, Lucas's cake selling business provided a greater reward in this case.

However, the amount of money that Sofia received depended on the amount of profit Lucas made, which increases the risk.

If Lucas had sold fewer cakes, he would have made less profit, so Sofia's rewards would've been lower.

So, for example, if the start-up cost was 500 pounds and Sofia's share was 20%, but Lucas only sold enough cakes to make 510 pounds, how much money would Sofia receive? Pause the video and see if you can work this out now.

Welcome back.

We should have calculated that Sofia will only receive 102 pounds, which actually means it's only 2 pounds more than she initially paid over.

Remember, if Lucas sold even fewer cakes, he could actually have made a loss, and then she would've got back less money than she invested.

So for example, what if Lucas only sold enough cakes to make 450 pounds? Well then, Sophia only gets back 90 pounds, which is 10 pounds less than she paid over.

So she's actually lost 10 pounds on this.

Now, there are other ways to invest money, especially when dealing with larger amounts, and these investments also come with varying amounts of risk and reward.

Some examples include purchasing property, stocks and shares, and cryptocurrency.

Some people invest by purchasing property, such as houses.

Now, average house prices increase and decrease over time.

Therefore, a house sale could lead to a profit or a loss depending on when it's sold.

So for example, you can see here on the graph, if I bought a house when it was quite expensive and then sell it when house prices have dropped, I'll make a loss.

If I sold my house here, however, I'd break even, because price average is about the same.

But what about if I sold up here? Well, then I'd make a profit, because the price I purchased the house for is less than the price that I sold it for.

However, there are many other factors that make property investment more complex than this, such as inflation and other costs involved in buying or selling houses.

Andeep invests 50 pounds into a savings account that pays 4% interest per annum.

After a year, Andeep withdraws his 50 pounds plus the interest it earned.

So how much money did Andeep withdraw? Pause the video and work this out now.

Welcome back.

Well, you should have worked out that Andeep withdrew 52 pounds.

Now, Andeep decides to keep his 52 pounds in the savings account that pays 4% interest per annum.

So a year later, Andeep withdraws this 52 pounds, plus the interest it earned.

So how much money did he withdraw? Pause and work this out now.

Welcome back.

Well, you should have said that he withdrew 54 pounds and 8 pence.

Laura wants to start her own small business selling badges.

The initial start-up cost would be 200 pounds, but Laura only has 150 pounds.

She invites Andeep to invest 50 pounds in her business for a share of the profits.

What would Andeep's share be? Pause and work this out now.

Welcome back.

Well, Andeep is investing a quarter of the start-up cost, so therefore he should get a quarter of the profits.

In other words, 25%.

So Laura now sells these badges for 230 pounds.

Andeep receives his initial investment back, plus his share of the profits.

So how much does he receive? Pause and work this out now.

Welcome back.

Well, Andeep will receive 57 pounds and 50 pence, which is his initial investment of 50 pounds plus 7 pounds 50 in profit.

What were the risks of this investment though? Pause and write this down now.

Welcome back.

And you should have said something along the lines of, Laura may not have sold enough to make a profit, or she might even have made a loss.

It's now time for the first task.

Question one, use a dice and a calculator to complete the following simulation over four years.

Your starting balance for year one is 200 pounds, and each year you choose whether to invest your money in one of the two options.

Option A, a savings account with 5% interest, where the reward is guaranteed.

So each year you invest your money here you increase your starting balance by 5%.

Option B, Lucas's cake shop, where the reward depends on how many cakes Lucas sells.

Each year you invest here, you roll a dice to determine whether you make a loss, break even or make a profit.

The chance of making a profit or loss does change from one year to the next.

Your end balance for each year becomes your start balance for the next year.

Use the following table to complete the simulation for four years.

And then repeat the entire simulation multiple times.

Here's the table that you can use, and you can see for option B what the different values on the dice lead to.

Pause the video while you run the simulation now.

Welcome back.

Now, what you can see here is just an example.

I chose to invest my money in option A every single time, so you can see how my end balance has changed.

In this example, I went for option B every single time, and I've written down what I rolled on the dice, so you can see what my final value ends up being.

And this example, you can see I went for a mixture of option A and option B.

What did you find was the better option? Maybe you saw it was option A, maybe option B.

That dice roll really affected it, didn't it? Let's look at the second part of our lesson now, on risks and rewards with borrowing.

Sometimes you may need or want to purchase something at a time when you do not have enough money to pay for it in full.

In these situations, you may choose to borrow money to make a purchase and then pay the money back later.

When borrowing money, you may be required to pay back more money than you borrowed.

In this situation, the lender receives back the money you borrowed plus interest.

Paying back over a longer period of time usually reduces how much you need to pay back in each instalment.

However, this also usually results in paying back more money in total.

So what might someone choose to borrow money for? Pause the video to have a quick discussion now.

Welcome back.

Did you say any of these? Well, if you went for some small to medium sized purchases, you could have said clothes, furniture, concert tickets, bicycle, just as some examples.

Larger purchases could be a car, a house, a holiday, repairing your boiler in your house.

Jacob has a part-time job that pays 36 pounds per week.

His bicycle breaks and he wants to buy a replacement.

He wants to buy one that costs 360 pounds.

He plans to borrow the money to pay for the bicycle and then pay it back over time.

What risks should Jacob consider when doing this? Pause and have a discussion now.

Welcome back.

You might have said something like, he might have to pay back much more than he borrowed.

And you're right.

He might not be able to afford the regular instalments of repayment.

And if he can afford the regular instalments, it might not leave him with very much money left over from his wages.

He might leave his part-time job or his income could be reduced.

Then he would not be able to pay off the rest of his debt.

He might need to purchase something else before he's finished paying for his bicycle, and he would not be able to afford it.

If he also borrows to pay for that too, he could end up with even more debt than he might be able to afford.

A credit score indicates how likely someone is to repay what they borrow, and borrowing money can affect your credit score.

If you borrow money and pay it all back on time, then it can improve your credit score, because it shows you're a reliable person to lend money to.

A good credit score means that lenders are more likely to let you borrow money from them.

They may also allow you to pay back with less interest.

Failing to pay back borrowed money on time can lower your credit score though, because it suggests you are not a reliable person to lend money to.

A bad credit score means that lenders are less likely to let you borrow money from them.

If they do lend you money, they may ask you to pay back more interest than a customer who has a better credit score.

Jacob has a part-time job that pays 36 pounds per week.

His bicycle breaks, he wants to buy a replacement that will cost 360 pounds.

He's offered three options to pay back the money.

Option A is pay back 360 pounds, interest free, within six weeks.

What could be a problem or a risk with this option? Pause and work this out now.

Welcome back.

Did you spot that over six weeks, he'll only pay back 216 pounds, which means based on his part-time job alone, Jacob can't afford to pay this back in time, so he would have to borrow money from elsewhere.

Option B is pay back 390 pounds in 12 weekly instalments.

Well, what might be a problem or a risk with this option? Pause the video and work this out now.

Welcome back.

Well, he's gonna be paying back 30 pounds more than he borrowed.

Now, if he pays it back in 12 weekly instalments, that's 32.

50 per week.

So Jacob can afford this, but that would only leave him with 3 pounds 50 a week from his wages for 12 whole weeks.

Option C is to pay back 450 pounds in 24 weekly instalments.

Well, what could be a problem or risk with this option? Pause the video and work this out now.

Welcome back.

Well, he's paying back 90 pounds more than he borrowed.

It's quite a lot.

Well, this does work out at 18 pounds 75 pence per week, So he could afford this and he would have 17 pounds 25 pence left from his wages each week.

However, it is a long period of time and something unexpected may happen, such as him leaving his job or needing to buy something else.

It's now time for our final task.

Question 1.

Aisha receives 10 pounds a week pocket money from her parents.

She can also earn up to 18 pounds a week from her part-time job.

She wants to borrow 160 pounds to pay for a trip, and she's presented with these three options.

What I'd like you to do, please, is write down at least one benefit and at least one risk for each of the options.

Pause and do this now.

Welcome back.

Question 2.

Lucas wants to start his own small business baking and selling cakes.

The initial start-up cost would be 500 pounds, but he only has 200.

So he's going to borrow 300 pounds on the condition that he pays it all back with 8% interest.

So part A, how much money would Lucas be expected to pay back? And part B, Lucas expects to sell the cakes for 550 pounds in total.

In this case, he would pay back what he owes and still make a profit on his initial 200 pound investment.

How much profit would he make? And then part C, what risks could there be with Lucas's plan? Pause the video and work this out now.

Let's go through our answers.

So for option A, one of the benefits could be that the combination of Aisha's part-time job and pocket money means she can afford the weekly repayments.

But one of the risks might be, it only leaves her with a maximum of 5 pounds 50 per week.

She'd be relying on earning at least 12 pounds 50 per week from her part-time job in order to pay each instalment.

For B, one of the benefits could be that she can afford the weekly instalments using just her pocket money, so she hasn't got to rely on her part-time job.

A risk could be she'll be making repayments for a long period of time.

Another unexpected expenditure may occur during that time.

An additional problem would be she'll have to pay back an extra 80 pounds in total.

For C, a benefit could be that she could potentially pay the full amount back within six weeks and not pay any interest at all.

But a risk is, if she doesn't pay the full amount within six weeks, she'll have to pay a very high rate of interest on the remaining debt.

Well done if you said any of these or came up with your other own sensible benefits or risks.

Question 2, for Lucas and his small business.

How much money would he be expected to pay back? Well, with 8% interest, that would be 324 pounds.

How much profit would he make? Well, when we take away what he's got to pay back from what he's going to make, that leaves us with 226 pounds.

His initial investment was 200 pounds, meaning he'll make a 26 pound profit.

But what risks could there be with Lucas's plan? Well, he might not sell enough cakes to make a profit, meaning he'll actually make a loss after paying back his debt.

He might not sell enough cakes to pay back his debt, which could lead to more interest charges or lowering his credit score.

Let's sum up what we've learned today.

Investing money can lead to rewards, such as receiving back more money than you invested.

However, investing money also comes with a level of risk.

Borrowing money can allow you to make purchases in situations where you're unable to pay the full amount at the current time.

And borrowing money comes with a level of risk.

Well done.

You've worked really well today.

I look forward to seeing you for more lessons in the future.

Goodbye for now.