A percentage is simply a type of fraction. It means “a part of proportion of 100”. They are often used to make a standard comparison between different amounts of change.
To express one number as a percentage of another we divide 1 fraction by the other and then make the denominator 100. Let’s try and making 42 a percentage of 53:
$$ \dfrac{42}{53} = 0.792 \color{red}{\times \dfrac{100}{100}} = \dfrac{79.2}{100} = 79.2\% $$
We can find the original value of something after a percentage change. We can do this by turning the question into one fraction over another. We make the total percentage change (100 add or subtract the percentage change) the denominator and then we make the denominator a percentage (out of 100). One way to do this is to multiply and or divide the fraction to get what we want, or we can find the numerator when the denominator is 1 and multiply the fraction by 100. Let’s find the original value of a TV which is now priced at $130 after a 25% increase:
$$ \dfrac{130}{(100 + \color{red}{25})} = \dfrac{130 \color{red}{\div 5}}{125 \color{red}{\div 5}} = \dfrac{26 \color{red}{\times 4}}{25 \color{red}{\times 4}} = \dfrac{104}{100} \therefore \$ 104 $$ $$ \text{ OR: } \dfrac{130 \color{red}{\div 125}}{125 \color{red}{\div 125}} = \dfrac{1.04}{1} \times \dfrac{100}{100} = \dfrac{104}{100} \therefore \$ 104 $$
Also, we can calculate percentage increase or decrease easily (another word for decrease is depreciated) we just have to remember a basic formula. $$ \text{ New value = Starting value } \times (100\% \pm \text{percentage change}) $$
For example a Mac computer was $1200 it then increased by 30% calculate the new value:
$$ \text{New value} = \$ 1200 \times (100\% + 30\%) = \$ \dfrac{1200}{1} \color{red}{\times \dfrac{130}{100}} = \$ \dfrac{(1200 \times 130) \color{red}{\div 100}}{100 \color{red}{\div 100}} = \$ 1560 $$
There are 2 types of interest; simple interest means the initial value is multiplied by the same amount and you must use the above method to calculate the new value, compound interest means, for example each year (or any time period) you reinvest what you made and get the same rate. Over time compound interest is far more profitable.
Here is the formula for compound interest:
$$ NV = IV \times (1 \pm r)^n $$
Where NV is the New value, IV is the initial value, r is the interest rate and n is the number of periods.
For example, each year a car depreciates by 3% in value, at the end of 2010 it was worth $10000. Work out the value at the end of 2005:
$$ NV = \$ 10000 \times (1 - 3\%)^{(2010-2005)} $$ $$ NV = \$ 10000 \times (\dfrac{100}{100} - \dfrac{3}{100})^5 = \$ 10000 \times (0.97)^5 = \$ 8587 $$
Another list with links to other websites
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