Percentages of $\$100,000\$6,200$ is $6.2\%$ of $\$100,000$. That leaves$\$93,800$ as $93.8\%$ of that $\$100,000$. But when I take$\$93,800$. and multiply it by $6.2\%$, I get $\$99,615.60$instead of$\$100,000$. Why is this? And how do I get back to my $\$100,000$. Do I need to multiply the$\$93,800$ by more? Why?

• When you do this, you are subtracting 6.2% of \$100,000; but then you are only adding back on 6.2% of \$93,800, which of course is less. To get back to \$100,000, you have to divide by 1-.062=.938 instead. Commented Aug 2, 2014 at 22:08 3 Answers You're thinking about it wrong. Sure,$\$93,800$ is $93.8\%$ of $\$100,000$. However, it doesn't mean that$106.2\%$of$\$93,800$ is $\$100,000$and as you saw, that's not true. You have to set it up like so: $$\93,800=93.8\%\text{ of }\100,000 \\ \implies \93,800=(0.938)(\100,000)$$ Now the question you're asking is - what times$\$93,800$ will give me $\$100,000$? In other words, what is$c$in this equation: $$c \times \93,800=\100,000$$ Using basic algebra, if you re-arrange the formula shown at the top, you'll see that: $$c=\frac1{0.938}$$ Giving you an approximate answer of: $$c=1\frac{31}{469}\approx 1.066098$$ And this makes sense. To get to$\$100,000$ from $\$93,800$, you'd need to add$100,000-93800=\$6,200$. What percentage of $\$93,800$is$\$6,200$? Well:

$$\frac{\6,200}{\93,800}=\frac{31}{469}\approx 6.6098\%$$

Meaning that you'd need to take $100\%$ of $\$93,800$in addition to$\approx6.6098\%$of it to get to$\$100,000$.

You need to multiply with $\frac1{0.938}\approx 1.0660980810234541577825159914712153518\ldots$, i.e. you have to add $6.6098\ldots \,\%$. For small percentages, you assumed method almost works (i.e is a good approximation), but the larger the percentagem the bigger the problem (i.e. the diffference to the correct method) becomes. For example, if you subtract $50\,\%$ (cut in half), you have to add $100\,\%$ (double) to get back to the original; and if you subtract $100\,\%$, you get zero and can add percentages as high as you want and wonÄt succeed ...

Instead of taking $6.2\%$ of $\$93,800$, you should be taking$6.2\%$of$\$100,000$.

Think of it as taking a percentage of the total amount, where the total amount in this case is $\$100,000\$.

Hence, $0.062\times100000=6200$ $0.938\times100000=93800$ And $6200+93800=100000$ No algebra is needed, just an understanding of what your taking a percentage of.