Hi, I'm Mrs. Wheelhouse and welcome to our series of lessons on maths and personal finance.

I'm really excited to look at this with you.

So let's get started.

By the end of today's lesson, you'll be able to calculate, evaluate, and select the most appropriate saving schemes and borrowing arrangements for given circumstances.

Now we're gonna be using some important words today, such as interest and the rate of interest.

Now, if those are unfamiliar to you, feel free to pause the video now and have a read through the definitions.

Now, a phrase you may not be familiar with is the annual percentage rate or APR, and this is the cost of borrowing money on a credit card or loan over a year and something we're gonna be using in our lesson today.

Now our lesson has two parts.

We're gonna begin by looking at borrowing with interest.

When we know how much something costs and there is no time pressure, it's possible to save money in order to buy the item.

But what happens when there is a limited amount of time? It is November and Sam's coat has just torn.

Oh no.

Sam doesn't have enough money to buy a new coat right now.

It will take Sam three months to save enough money to buy the new coat that they want.

So it's not a case of getting a coat.

Sam could do that, but Sam wants a particular coat.

Hmm.

Now why might waiting not be a good idea? Pause the video and have a think now.

Welcome back, what did you say? Well, you might have said that, "The weather may have changed and a coat may no longer be needed," and, "the shop or shops may have stopped selling the coat as well." So, what are Sam's options? Well, Sam could save for the coat, but it might not be available or needed in three months time.

Sam could borrow some money to buy the coat or Sam could buy a cheaper coat, but the quality will be lower.

In Sam's situation, they may have to borrow money.

This was not planned for as the coat tearing was not expected.

Unplanned borrowing may mean that Sam has to pay the money back with interest.

Let's do a quick check.

I'd like you please to match the word or phrase with the correct definition.

Pause the video and have a go at this now.

Welcome back.

You should have said that interest is money added to savings or loans.

Simple interest is always calculated on the original amount.

Compound interest is calculated on the original amount and the interest accumulated over the previous period, which means that rate of interest is the percentage by which an amount will increase.

Well done if you've got those all right.

Sam has £40 that they can put towards buying the coat they want.

Sam needs to borrow another £40.

Let's consider two possible loans that Sam could take.

Loan one, borrow £40 and pay back £40 plus 3% interest after one month.

Or loan two, borrow £40 and pay back £10 plus 1% interest on what is owed each month.

Which loan should Sam take? Pause the video and have a think now and pick which one you think Sam should take.

Welcome back.

Well, let's use maths to work out which loan is the best one for Sam.

So begin by looking at the example.

Let's say Sam wants to borrow £60 and pay back £60 plus 4% interest after one month.

How would we calculate this? Well, the amount to repay is £62.

40.

It's now your turn.

Let's consider loan one where Sam's borrowing £40 and paying it back plus 3% interest after one month.

How much will Sam need to pay back in total? Pause the video while you work this out now.

Welcome back.

We should have said that Sam's got to repay £41.

20.

Now let's consider an example to help us with loan two.

We're gonna borrow £60 and pay back £15 plus 3% interest on what is owed each month.

So, in the first month, I've got to pay back £15 plus 3% interest on what was owed.

Well, at the start of the month, I owed £60 and 3% of that gives me £1.

80.

So I add that onto the £15.

Now, month two, I've got to pay back £15 and what's remaining on the loan.

Well, I paid off £15 of the loan before, so I've got £45 of the loan left to pay back.

So I calculate 3% interest of that and add it on, which gives me £16.

35.

And I repeat that for the other two months.

So in other words, paying back £15 and then 3% of what is owed on the loan.

So that interest that I'm accruing, it's not coming off of the main loan.

So, in total, how much I got to pay back? I've gotta pay back £64.

50.

Now using that example to help you, let's consider loan two where Sam wants to borrow £40 and has to pay back £10 each month plus 1% interest.

Pause the video while you have a go at this now.

Welcome back, let's go through each month.

So month one should be £10.

40, month two £10.

30, month three, £10.

20, and month four, £10.

10.

Therefore, altogether Sam will have to repay £41.

So which loan should Sam take? Well, as you can see, there isn't a lot in it, but it should be loan two.

The most important thing however to note is that in both cases, Sam had to pay back more than they borrowed.

If Sam's savings had been enough, then they would not have needed to borrow that money.

Some expenditures are unexpected and savings may not be enough to cover them.

Let's look at our first task now.

Question one.

Sophia has just seen that a new VR headset has been released.

It costs £530 to the nearest pound and Sophia has £110 saved up.

Consider the information on the next slide and help Sophia decide what she should do if she wants to buy the headset.

So she has option A.

She receives £20 a month as pocket money.

She could save this each month until she has enough money to buy the headset.

Part B gives us two other options.

She could borrow the money and either pay back the full amount, plus 4.

2% interest, it is assumed she pays back £20 a month until her debt's cleared.

Or she could take the loan that lets her pay back £20 per month for the first year interest free and then pay back the remaining amount, plus 7% interest on what remains, still paying £20 back per month.

So what should she go for? Pause the video while you consider which option is best for her.

Don't forget to justify your answer by doing some calculations.

Pause the video and have a go now.

Welcome back, let's see what you put.

So I'm gonna go through and show some examples of what you may have written.

So for part A, Sophia needs to save £420.

In this scenario, it's going to take her 21 months or one year and nine months, to save up enough money.

This is a very long time, so it is not a viable option if she really wants to buy that headset.

B, part i.

Remember she wants to borrow £420.

In this scenario, she'll be paying back £437.

64.

It's gonna take her 22 months to do this.

Now this is a long time, but it will allow her to buy the headset now.

For B part ii, she needs to borrow the £420 and she pays back £240 in the first year.

She's then got to pay back the remaining amount, plus 7% interest.

So in total she pays back £432.

60.

It will also take her 22 months to do this.

It's the same length of time, but it's actually £5.

04 cheaper.

So regardless of the options, it's gonna take her between 21 and 22 months to either buy the headset or pay off the loan she used to buy the headset.

She needs to decide how important the headset is to her and whether it is worth it, given how long it will take her to afford it or pay for it.

Now all calculations were made assuming that Sophia could reliably pay back £20 per month.

But what if something were to happen and she couldn't pay that? In that case, although B part ii was the better option because it was slightly cheaper, when she considered the loan, it might not be, if she couldn't reliably pay back the £20 per month when it was interest free.

Something to consider.

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

We're gonna look at big purchases.

Saving money is useful for when there is an expense that needs to be met.

However, some expenses are so great that saving may not be practical in a given timeframe.

Alex is visiting his cousin who lives in the top flat of a building.

Alex notices that there is a damp patch on the ceiling.

Why might this cause concern? Pause the video and have a think now.

Welcome back.

Did you say something like this? Well, "Since Alex's cousin lives in the top flat, the ceiling is also the roof of the building.

If there's a damp patch on the ceiling, it may be that there's a hole in the roof." A roofer is called and they can confirm there is a hole that needs to be fixed.

However, upon inspection, there are significant problems with the roof due to its age, and it needs to be replaced.

Alex's cousin has three choices here.

They could choose to not fix the leak.

They could choose to fix only the leak, or they could choose to replace the whole roof.

What do you think should be done? Pause the video and have a think now.

"Ignoring the leak won't stop it and the contents of the flat may get damaged.

That would be more expensive," points out Alex.

So not fixing that leak, and just ignoring, it isn't gonna help.

In fact, it may be worse in the long run.

Now fixing just the leak will cost £400 and replacing the whole roof will cost £6,000.

My cousin has enough money saved that he could pay to fix the leak.

He would have to take out a loan to replace the roof.

What do you think should be done? Has your answer changed from before? Pause the video and have a think now.

Let's do a quick check.

True or false? Fixing the leak only is the right thing to do as Alex's cousin has enough money saved to pay for this.

Do you think that's true or false? And don't forget to justify your answer.

Pause the video and make your choice now.

Welcome back.

You should have said that's false.

There's no definitive right thing to do here.

Replacing the roof puts Alex's cousin into debt, but fixing the leak only means the underlying cause has not been addressed, so there are likely to be more leaks in the future.

The roofing company offer the following loan to customers.

Borrow £6,000 with a no interest loan for the first 12 months, followed by 12.

9% APR.

The bank offer the following loan to its customers.

Borrow £6,000 and repay the loan over five years at 7.

2% APR.

So which loan is better? Now you might initially think that it'll be the one with the lower interest rate.

However, with that no interest for the first 12 months, maybe that would be better.

What do you think? Pause the video and have a think now.

Welcome back.

Let's do some maths to work it out.

So with this loan, what's the minimum amount that will need to be repaid? Well, that's £6,000.

If the loan could be repaid in the first 12 months, then no interest is added.

With the bank, this means Alex's cousin "will have to pay back £6,432." Is Alex right with that statement? No, he's not.

He'd be correct if it was simple interest, but that is not how this sort of interest works.

The annual percentage rate is the cost of borrowing money on a credit card or loan over a year.

To make sure you stay on track with paying back your loan, you may be required to make monthly payments.

Estimating monthly repayments can be done using this formula.

Where P is the monthly payment, a is the total loan amount, r is the monthly payment rate, which is found by dividing the annual rate by 12, and n is the total number of monthly payments.

In other words, the amount you have to pay back each month will change based on how long you've got the loan for.

So, let's look at what's actually going to be paid back each month.

So we want total loan amount.

Well, in total we're borrowing £6,000.

So let's substitute.

There we go.

Now let's consider the monthly repayment rate.

Well, the repayment rate is 7.

2%, but that's for the year.

You need divide by a hundred and then divide by 12.

There's our rate.

And then the total number of monthly payments.

Well, we've got it for five years, which means a total number of months is 60.

And now we can work out what the monthly payment will be, and we can see what the monthly payment will be here, as an estimate.

I'd like you please to use the formula to estimate the monthly repayments if we're borrowing £10,000 and repaying the loan over 12 years at 5.

7% APR.

Pause the video while you work this out now.

Welcome back, let's see how you got on.

What you could see now on the screen is what your formula should have looked like if you did the substitution correctly, and then as an estimate, this will be £96.

04 per month.

Well done if you got that right.

It's now time for your final task.

It is late June and the boiler that heats Aisha's home needs replacing.

It will cost £4,380 to do this.

Assuming the boiler will be replaced at the start of November, calculate the average amount of money that needs to be saved each month to meet this cost.

Pause and do this now.

Part B.

The gas company offer a deal.

They will lend the money and there is no interest to pay for the first 12 months.

Calculate the average amount that should be paid back each month so that the loan is paid off in those 12 months.

Pause and do this now.

Part C.

After 12 months, any remaining money still owed to the gas company has an interest rate of 3.

2% APR and it must be paid off over two years.

Assuming nothing has been paid off in the first 12 months, calculate an estimate for the monthly repayment amount.

Pause the video and work this out now.

Part D.

By considering your answers to parts A to C, explain the positives and negatives of each option and state which option you recommend and why.

Pause the video and work this out now.

Welcome back, let's go through our answers.

So part A.

Calculate the average amount of money that needs to be saved each month to meet the cost.

Well, the only months we can save are July, August, September and October, which means that we need to save £1095 per month.

Part B.

If we take this deal then it means that each month we've got to pay back £365.

Part C.

If we paid off nothing, we want an estimate for the monthly repayment amount and that would be £188.

65.

Well done if you got that right.

So, for Part D, I've just given an example of what you could have written.

Remember you had to consider the positive and negatives of each option and say what you'd recommend and why.

So, I considered, first of all, the saving option.

Well, it meant there was no debt, but it does require needing to save over a thousand pounds each month.

That is a lot of money to save and it may not be practical.

Now, part B, the gas deal, if you can pay it off in the first 12 months, it's much more affordable because it only costs £365 a month and you only pay what is owed 'cause there's no interest.

However, that might still be too expensive.

And then in part C, where you've got the gas deal with interest, well, that was only £188.

65 per month and it's far more affordable.

And this is assuming no money's paid off in the first 12 months.

So actually, that value could be a lot lower.

It does though, mean that you're in debt for three years.

So this was my recommendation.

Given that the boiler needs to be replaced, I'd recommend that Aisha's family save what they can during the months July to October.

They can then pay what they can towards the cost of the boiler and use the gas deal, option B, to cover the rest of the cost.

They should then try to pay the remaining money back before the end of the 12 months.

This reduces what is owed so that the amount that interest might be applied to is as small as possible.

Well done if you said something similar to that.

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

Certain situations may require planned saving or borrowing.

Interest rates, and my circumstances, will affect my choices.

Saving schemes or borrowing arrangements need to be analysed to determine the most appropriate choice for my circumstances.

Remember what's right for you may not be the same as what's right for someone else.

Planned and organised saving or borrowing over extended periods of time can be useful when managing my money effectively.

Well done, you've worked really well today.

I look forward to seeing you for another lesson in the future.

Goodbye for now.