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 then of today's lesson, you'll be able to describe why insurance is important and identify situations where insurance may be needed through calculations.

Now, insurance is a means of protection from financial loss.

We're gonna be using that word an awful lot today.

Our lesson is broken into two parts.

We're gonna begin by considering buying insurance.

Andeep is considering buying a phone.

"Oh, there's so much choice.

Should I buy a cheap phone or more expensive phone?" Well, Sofia says, "If you're going to buy a more expensive phone, you should consider buying insurance for it as well." "What? The phone's already expensive," says Andeep, "Why would I pay more money?" Well, insurance is a means of protection from financial loss and levels of insurance differ.

But it is common that whilst you have insurance, any costs covered by the insurance would be paid for you.

So Andeep says, "Insurance would mean that if my phone breaks, I would get the money back?" And Sofia says, "Well, yes, as long as the insurance says so." And you do need to read the terms and conditions of your insurance very carefully.

So insurance for phones normally helps with the cost of replacing or repairing the phone in the event that it's damaged, stolen, or lost.

So quick check now.

True or false.

Having insurance means that, whatever money you spent, you will always get that back.

Is that true or false? And don't forget to justify your answer, please.

Pause and do this now.

Welcome back.

Did you spot that it's false? Well done if you did.

It does depend on what the insurance states that it does cover and how much cover it provides.

Remember, we do have to check this carefully.

Andeep is looking at a phone which costs 81 pounds and 99 pence and is considering whether to purchase insurance.

He's considering two different offers.

Offer one is pay five pounds per month for 18 months and offer two is pay 40 pounds initially followed by four pounds per month for 12 months.

So which is the better offer do you think? And why? Pause the video while you discuss this now.

Welcome back.

Now, before you do any type of calculating, you might have said offer one is better because it covers you for more time.

So 18 months versus 12.

You may, of course, have done some calculations.

Let's explore this.

Well, for offer one, let's consider how much will this insurance cost Andeep, and at what point will he have paid more for insurance than for the cost of the phone.

Pause the video now while you work this out.

Welcome back.

So how much will this insurance cost Andeep? Well, if it's five pounds per month for 18 months, it will cost him 90 pounds.

After 16 months, Andeep will now have paid more for insurance than for the cost of the phone.

Now let's consider offer two.

And again, please answer, how much will this insurance cost Andeep and at what point will he have paid more for insurance than the cost of the phone? Pause the video and work this out now.

Welcome back.

Well, the insurance will cost Andeep 88 pounds.

And after 10 months, he'll have paid more for insurance than for the cost of the phone.

So offer two is cheaper overall, but offer one is cheaper in the short term.

It really depends on whether Andeep will need to repair or replace his phone.

It's time for our first task.

Andeep is given money for Diwali and uses it to buy a new phone for 130 pounds.

His family think he should buy insurance for his new phone and there are three insurance offers available.

Offer one, pay eight pounds per month for two years and the insurance will pay out 130 pounds if the phone is damaged, lost, or stolen.

So for part A, how much will this insurance deal cost Andeep? And for part B, state when this offer stops being useful.

Pause the video and work this out now.

Welcome back.

Let's look at offer two.

Here, you pay five pounds per month for 30 months.

And again, the payout is 130 pounds if the phone is damaged, lost, or stolen.

So part C, how much will this insurance deal cost Andeep? And part D, state when this offer stops being useful.

Pause the video and work this out now.

Welcome back.

Let's look at offer three.

Pay 40 pounds initially and then three pounds per month for 30 months.

And the payout is 130 pounds if the phone is damaged, lost, or stolen.

So part E, how much will this insurance deal cost Andeep? And part F, state when this offer stops being useful.

Pause the video while you work this out now.

Welcome back.

Time for question two.

Draw the graph for each insurance offer on the axes.

So offer one, offer two, and offer three.

Pause the video and do this now.

Welcome back.

Question three.

Using your answer to question two, explain to Andeep whether he should buy insurance or not.

If he should buy insurance, explain which offer is best for this situation.

Pause the video while you do this.

Welcome back.

Let's go through our answers now.

Question one.

How much will offer one cost Andeep was 192 pounds, and the offer stops being useful after 16 months.

For offer two, it will cost Andeep 150 pounds and this offer stops being useful after 26 months.

And offer three, it will cost him 130 pounds, so the offer never stops being useful because he's never gonna have to pay more than he initially paid for the phone.

Question two, I asked you to draw the graph for each insurance offer on the axes, so you can see for each month how much it's going to cost.

Question three.

I asked you to use your answer to question two, so these graphs, to explain to Andeep whether he should buy insurance or not.

And if he should, which offer is best? Well, offer one should never be chosen because there's always a cheaper alternative.

The graphs for offer two and three show this as at least one of them is always lying below the graph for offer one.

Offer two should be chosen if Andeep thinks he's likely to break or lose his phone in the first 20 months because that's when it's the cheapest.

If he thinks he's more likely to break or lose his phone in months 21 to 30, then he should choose offer three.

So Andeep should buy insurance if he thinks it is likely he will break or lose his phone.

He should go for offer two if he thinks this is more likely to happen in the first 20 months, and offer three if he thinks this is more likely to happen after the first 20 months.

It's now time for the second part of our lesson on making comparisons.

Andeep's dad buys a new smartwatch and a new TV.

The smartwatch costs 100 pounds and the TV costs 800 pounds.

Andeep wants to know whether his dad is going to buy insurance for the new items. Insurance for the smartwatch costs 10 pounds per month and should the watch stop working will either pay for it to be fixed or for it to be replaced.

Insurance for the TV costs 15 pounds per month.

And should the TV stop working, will either pay for it to be fixed or for it to be replaced.

So which do you think is the better option? Pause the video while you discuss this now, and don't forget to justify your answer.

Welcome back.

So what did you think the better option was? Well, I've said after 10 months, the insurance for the smartwatch will have cost 100 pounds, which is the cost of the watch.

So if the watch is damaged during the first 10 months, then the insurance might be worth buying.

After 53 months, so that's four years and five months, the insurance will have cost 795 pounds, which is just under the cost of the TV.

After 54 months, it will have cost 810 pounds, which is just over the cost of the TV.

So if the TV is damaged during the first four years and five months, then the insurance might be worth buying.

Andeep says, "We should ensure the TV.

The TV is the more expensive item and we can insure it for longer." Do you agree with Andeep? Pause the video while you discuss this now.

Welcome back.

Did you agree? Well, when considering whether to buy insurance for an item, we should consider the following.

The cost of the item.

How expensive is it to replace? The cost of the insurance.

Is there a fixed length we have to buy it for? What's the likelihood of needing to use the insurance? So is it likely that the item will be damaged and need replacing? Remember, insurance is a means of protection from financial loss.

At the moment, ensuring the TV seems to be a good option and better than ensuring the smartwatch.

Let's look at how likely it is that each item will be damaged and need replacing.

Well, Andeep says, "The TV is in our living room and in a corner.

It is unlikely to be damaged.

The smartwatch will be worn every day and my dad is very into his sports.

He broke his last smartwatch after only owning it for three months." Ah.

Now you've got that information, which do you think is the better option? And again, justify your answer.

So it might have changed from before, but it might not have done.

Pause the video while you discuss this now.

Welcome back.

Well, it seems unlikely the insurance will be needed for the TV, but very likely it'll be needed for the smartwatch.

So maybe we should be ensuring that.

It's now time for our final task.

Question one, you are considering whether to buy insurance for the following items. So a bike that costs 160 pounds, a laptop which costs 580 pounds, and a gaming console that costs 390 pounds.

Due to your finances, you can only buy insurance for one of these items. Consider the following insurance deals and select one and justify your choice.

So for the bike, the cost is six pounds per month and you must have the insurance for three years.

If lost, damaged, or stolen, the insurance will pay for a bike of an equivalent cost.

For the laptop, the cost is 10 pounds 99 per month, and the term length is five years.

If lost, damaged, or stolen, the insurance will pay for a laptop of equivalent cost.

And the gaming console, the cost is six pounds 80 per month and the term length is four years.

Now if lost, damaged or stolen, the insurance will pay for the same make or model.

So pause the video now while you work out which one of the insurance deals you should go for and justify your choice please.

Pause the video while you work this out now.

Welcome back.

Let's go through this.

So which one are we going to pick? And don't forget, we have to justify.

So let's start by considering the bike.

Well, this insurance deal would cost us 216 pounds.

This is 135% of the original cost of the bike.

The insurance would pay for a bike of equivalent cost.

So it's likely a new bike could be bought if something happens to this one.

A bike may be used often and left unattended in public spaces, so it's what we'd call a high risk item.

Now for the laptop, the insurance would cost us 659 pounds and 40 pence, and that's 114% of the original cost.

The insurance would pay for a laptop of equivalent cost, but would this mean a better machine or a worse one? Hmm, and if the laptop's outside of the home, it increases the risk, but if I keep it at home, it could be quite a low risk item.

Now the gaming console, this is only 84% of the original cost.

That seems pretty good.

Now the insurance would pay for the same make or model, but remember, gaming consoles can become outdated very quickly.

It is very unlikely that this would leave the home, so it's a low risk item.

So you might have said something like the following.

The insurance for the console does not seem to be worth it, given how quickly consoles become outdated and it is a low risk item.

The insurance for the laptop seems the best deal if we're taking the laptop outside of the home because that increases the risk that something might happen to it.

The insurance for the bike would be the better deal if the laptop is not being taken outside of the home because our bike could be left unattended in public spaces and might be stolen.

So remember, these are just examples of what you might have said.

You could have said something different and it'd be equally valid.

Well done.

It's time to sum up what we've looked at today.

Insurance is a means of protection from financial loss.

Insurance may cost more than the original cost of the item in the long term, but it may also cost less.

Insurance means avoiding a sudden large expenditure that was not planned for.

And this can help with your financial security.

Well done.

You've worked really well today.

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

Goodbye for now.