Video: AQA GCSE Mathematics Foundation Tier Pack 4 • Paper 1 • Question 5

A bank charges a fixed fee of £5 for every day spent in an unarranged overdraft. Simon goes into his overdraft on the 29th of January and pays it off on the 7th February. Calculate the total amount that Simon is charged for the time that he spends in his overdraft. Assume that he is charged for the day that he enters the overdraft and the day that he pays it off.

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Video Transcript

A bank charges a fixed fee of five pounds for every day spent in an unarranged overdraft. Simon goes into his overdraft on the 29th of January and pays it off on the seventh of February. Calculate the total amount that Simon is charged for the time that he spends in his overdraft. Assume that he is charged for the day that he enters the overdraft and the day that he pays it off.

So what we’re told is that he’s charged for the day he enters the overdraft and the day that he pays it off. So what this means in real terms is that he is going to be charged for the 29th of January and the seventh of February as these are those two days. So now, let’s work out the charge. So first of all, what we’re gonna do is start with January. And what we want to work out is how many days in January that Simon was charged for. Well, to help us work this out, there’s a rhyme that we’ve used many years over in schools. And that is to help us decide how many days there are in a month. And we know that 30 days hath September, April, June, and November. All the rest have 31 except for February alone, which has 28 or 29 on each leap year.

So from that, we know that January falls into the category of others. So it’s going to have 31 days. So therefore, he’s going to be charged for the 29th, 30th, and 31st of January, remembering that we include the 29 because that’s the day that he went into his overdraft. So therefore, he was charged a total of three days in January. Okay, great. So now, let’s take a look at February.

So in February, he’s gonna be charged for the first, second, third, fourth, fifth, sixth, and seventh, remembering that we’re including the seventh because that’s the day that he pays off the overdraft. And we’re told that he’s charged for that. So therefore, we can count and see that Simon has been charged for seven days in February. So therefore, the total number of days that Simon is gonna be charged for is the three days in January plus the seven days in February, which is equal to 10 days. Well, have we finished here? Well, the answer is no because the question doesn’t ask us how many days Simon was charged. It asks how much is the total amount that Simon is charged for the time that he spends in his overdraft.

So now, to work out the total amount that Simon is gonna be charged, we need to work this out by multiplying 10, because that’s the total number of days that he was in his overdraft, by five pounds. And that’s because we’re told that the bank charges a fixed fee of five pounds for every day in an overdraft, which’s gonna give a total of 50 pounds. So therefore, we can say that Simon is going to be charged 50 pounds for going into his overdraft on the 29th of January and paying it off on the seventh of February.

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