In this video, we cover the AQA GCSE Maths topic of financial maths which is needed for all jobs, from calculating wages to working out profit, loss and VAT. Knowledge of financial maths is also required to be able to understand bank statements and savings. We discuss subtopics like gross pay (the full amount paid to an employee before any deductions are made), deductions (income tax, national insurance and sometimes pension contributions) and net pay (what's left after deductions have been made from gross pay. This is the amount an employee actually receives).
We are looking at financial maths. So there are four main topics we'll cover and then we'll do a couple of example questions to finish off. So let's first look at salary and pay. Well, this is often represented by, you know, if we're converting, say, hourly wage into weekly salary. So let's say we earn, I don't know, 12, we want to work out how much we earn in a week.
Well, very simple, straightforward. We can work out how much we earn in a single day. That's going to be our hourly rate, times the number of hours we work, that's going to be this 12 lb/hour times 8 hours, and that's going to give us 96. So it's £96 that we earn in a day. If we do four days per week, where we just take our daily rate of £96 and we times that by four, which in this case will give us $300 and test my mental matter 360.
Hopefully. Let's look at profit and loss next. So let's say in this case, let's say we're an entrepreneur, right? We're going to spend £10 on Mars buyers, so we're going to spend £10 and we're going to buy 20 miles bars, right? Some discount shop has a deal on and they're offering 20 miles bars for £10.
And let's say we get to school and we sell all 20 miles bars, we decide to price them as 80 p each, so they're kind of 0.8 lb/bar. We want to work out what is our profit from this entrepreneurial endeavour. Well, in this case, we can work out how much we have in the bank leftover, right? So what's going to be our total revenue from this business? So if it's 0.8, it's 20 bars.
All we do is we take our price per bar and we time that by 20 bars. Eight times 20, we can make the slide easier for ourselves, we can times this by ten and divide this by ten. It's the same personal answer that we just make a lot easier. We get £16. The little trick we can do that is that our profit, though we've now got £16 in the bank, but we spent £10 initially, right?
We went down by £10 initially and we've now gone up by £16. So our actual profit is the difference between those two values. We've actually only made £6, so we've got a profit of £6. So depending on how much you want the £6, that may or may not be worth buying 20 miles bars. Interest rates.
There are two types of interest rates. We'll look at the nice one first. Simple interest rates, as I suggest, this is very simple to calculate. Let's say we put £100 into a bank and the bank gives us 6% interest per year, simple interest. But after year one, after the first year, we're going to have £106.
After year two, again, we calculate, based on our initial investment, how much we need to add on per year. So in this case, one of £112 after the third year, after year three, again, we just add on 6% of our initial investment, or 6% of 100. Again, it's just £6. So we add on £6 every time we're doing more after year four, obviously, we just add on £6. Again, we get one, two, four and so on.
That's simple interest, right? We just take our initial investment and we add that on the interest of that on every single time. Compound is slightly trickier, let's say. Again, we put £100 into a bank account and that account offers 6% compound interest. Well, in this case, after the first year, we just look at what we had initially at the start of that year and we work out an extra 6% on top of that.
So in this case, it's going to be £106.
The two types of interest diverge is in the second year, right? In the second year, we look at what we have at the start of that second year. This is kind of what we have on midnight on December 31, or midnight at the very start of January 1, we take this initial amount and we work out 6% of that. So, 6% of this. Well, the way we can do this is we take our amount, we take 106% and we times it by 1.6%.
That's technically what we're doing to work at 6%. This is our original amount and this is our plus 6% on top of the right, if we just times it by one, we end up with the original amount terms of 126. We add on that. And so if we do that on a calculator, 106 times 1.6%, we end up with 112.36. So £112.36 p, we could do another one.
So we take what we have after this year and we time that by 1.6%. We work out 6% on top of this. And so we do 112.36 times 1.6 and we can do that on the calculator. I'm going to be very lazy again. One one 2.36 times 1.86, we end up with one one 9.1 and we can keep doing this.
But you can already see, comparing the year three for both of them, we've got an extra pound in this account. What you can see we're doing here, typically what we're doing is we're taking our initial amount of £100 and we're taking this and we're timing it by our percentage change. In this case as a decimal, this is 1.6%. We're adding an extra 6%. So times this by 1.6% and then we take this amount.
This new amount in this case is £106. We take this whole thing and we times it by $1.6. And again, to work out the amount that we haven't third yet, we take this whole thing and we time this. In this case, it's £112.36. We times this by 1.6.
And what you can see happening is if we were to look at what this can be represented as. This is just 1.6 to the power of three, right? It's 1.6 times itself. Three times. And so, in general, we can take our initial amount and times it by our change to the number of years to the end to the number of years that we're interested in.
And that's going to be our kind of formula going forwards. Let's look at VAT. Finally, to finish off this group of subtopics VAT, let's say you've got a TV, and TV in the shop is showing a price of £480 and it's including the at. Well, the 80 is 20% at the moment in the UK as of 2020. So if we wanted to work out the original price of this TV, well, if I want to look at how we work out VAT, well, we take our initial price without VAT.
And if we want to add on 20%, we just times it by 1.2% and that gives us our final price. I can reverse this, I can work backwards, I can take my final price and I can divide it by 1.18 and I should be able to get my initial price right. I'm just dividing both sides by 1.2 and that gives me my initial price. So both of these formulas are going to be fairly important to VAT. In this case, if I'm working backwards, I'm given my final price.
I want to work out my initial price. So I can take 480, I can divide it by 1.2 and that's going to give me if I do my head, that's going to be £400.
That would be my initial price. Let's do a couple of exam style questions to finish off. Sarah works for a company. Her number. AP is 15.
She works 7 hours and gets overtime for each extra hour past her regular seven hour day. So if she gets an extra third of her normal rate and she does 10 hours, what is she going to earn? So if this is an extra third, while her number is £15, third of 15 is five, this is going to represent £20. Right. This is going to be her hourly rate for overtime.
And so what we're doing is we're taking our regular rate of £15. We times that by 7 hours. For the first 7 hours, she does 10 hours in total, so she's going to have 3 hours. The last 3 hours are going to be 20. So 15 times seven, that's going to give us, and 20 times three, that's going to give us 60.
So in total, she gets £165. Do you want to see more questions? Ed's profit on good luck cards in 2018 was £360. This is a decrease of 20% on his profit in 2017. What was the profit on cards in 2017?
Well, this is just like we did with VAT, right? It's very similar. And so we can take our final amount, we can divide it by 1.2%.
Actually, let's just double cheque. I'm not doing this thing right. We know that if it's a decrease of 20%, we take our initial amount. And if we're taking off 20%, we're left with 80%, right? We're left with zero 8%.
And so that's going to give us our final amount. But we're working backwards now, right? We've given our final amount in 2018. We want to work out our initial amount in 2017. What we need to do is we take our final amount, we rearrange this, we divide it by 0.8, and that's going to give us our initial amount.
In this case, we're doing 360 divided by 0.8. And again, I'm very lazy. Do that on the calculator, I end up with $450.
That would be our answer.
Next question. You deposit £400 into a bank account, paying 5% simple interest per year. How much interest would you earned after three years? So, again, this is fairly similar to what we've seen before, right? Simple interest in this case.
So what we do is we take our £400 and if we are adding on 5% every year, what's? 5% of 405% of 400 is just zero point nor five times 400, right? That's 5% as a decimal. There is a decimal to fractions to percentages video you can watch on same YouTube channel. So give it a look.
If you're not sure how that conversion works. We work out 5% of 400. Again, I can do my trick, right? I can times this by 100 and divide this by 100. All I'm doing really is five times four, right?
And I end up with £20. So that's my percentage interest for three years. It's just going to be 20 times three to give me £60. So my answer is going to be 60. And that's the end of financial maths
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