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This is very basic but struggling with coming up with an answer and would appreciate the help.

Given an amount + fee (0.25% on amount), how can I work out what the remainder of the fee is so that both fees work out to exactly 0.5%(tf) of the total amount?

As an example: 1. (0.005 - (0.005*0.005)) = 0.004975 2. (0.004975 * 0.0025) + (0.004975 * 0.0025) does not equal 0.005. We can control the second part and make it a little bit more to get the fee to be exact but not sure by how much exactly?

Another way to express it with a story would be: if someone wants to buy exactly 1 USD worth of apples and we say that we will take 1 - 0.5% and then go and buy an apple so that they pay exactly 1 and receive 1 - 0.5%. But the person we buy the apple from takes 0.25% on top of what we give them. So to ensure we don't charge them more than 1 and get our share, we need to subtract the 0.5% before we give it to the person selling the apples. They then take the amount we gave them and add their fee on top so we end up with (1 - (1 * 0.005)) = 0.995 + (0.995) * (0.0025) = 0,9974875.

Now we know that our final fee should be 0.5% of 1 but let's say the person selling the apple says actually, I only have 0.7 worth of apples so I will only charge you 0.7 + (0.7 * 0.0025) = 0,70175. We can't then go and do (0,70175) + (0,70175 * 0.0025) = 0,703504375 Because 0,703504375 - (0,703504375 * 0.005) != 0,703504375 - (0,703504375 * 0.005). It is 0,6999868531

So my question is how can we work out the above so that the fee they pay is exactly 0.5% of the total amount.

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1 Answer 1

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If I understand your question correctly, say a bill is $\$1000$, we first have a fee of $0.25\%$ which comes out to $\$1002.5$. We then want to know what the second fee percentage will be for the bill to be $\$1005$, that is $0.5\%$ more.

$\frac{1005 - 1002.5}{1002.5}\cdot 100 = .24938\%$

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  • $\begingroup$ The problem is that we don't know that the bill is 1005. We just know that we paid $1000 + 0.25 (percent). So in the formula above, we need to know the total amount $1005 and in this scenario we won't have it. Does that make sense? $\endgroup$ Aug 21, 2018 at 18:53
  • $\begingroup$ So you know you paid $1000 + 0.25\% = \$1002.5$ and from this you want to determine the amount $\$1005$. well, $1002.5\cdot 1.0024938 = \$1005$ $\endgroup$
    – Phil H
    Aug 21, 2018 at 19:41
  • $\begingroup$ Isn't the 1.0024938 dependant on the calculation on the left so it won't always be 0.24938 right? $\endgroup$ Aug 22, 2018 at 5:03

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