# Given we want to charge 0.5% of the total but we don't know what the total is, just what we paid.

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.

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.$\frac{1005 - 1002.5}{1002.5}\cdot 100 = .24938\%$• 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? Aug 21, 2018 at 18:53 • So you know you paid$1000 + 0.25\% = \$1002.5$ and from this you want to determine the amount $\$1005$. well,$1002.5\cdot 1.0024938 = \$1005$ Aug 21, 2018 at 19:41