3. Percentages

Applications; return on investments, credit card interest rates. Percent - means out of 100.

Questions:

What's 5% of 50?

If we increase 50 by 5% how much have we got?

If we decrease 50 by 5% how much have we got?

5% means 5 out of 100, which is $\frac{5}{100} = 0.05$, so 5% of 50 is $0.05 \times 50 = 2.5$.

Increasing 50 by 5%, means adding 2.5 to 50, giving 52.5.

Decreasing 50 by 5%, means subtracting 2.5 from 50, giving 47.5.

In general, if the initial amount is P₀, then X% of P₀ is $P_0 \times\frac{X}{100}$ and an X percent change in P₀ is found by calculating

$$P_0 + X/100 \times P_0 = (1 + X/100)\times P_0.$$

Given two numbers, calculate the percent change:

Example: Daily percent return: $100 \times \frac{Today - Yesterday}{Yesterday}$.

Today = 123, Yesterday = 114. Change (123 - 114)/114 = 0.0789. Percent change is $0.0789 \times 100 = \textcolor{green4}{7.89\%}$.

Example: closing price of IDTC over the last 4 days (check these):

 

Table 1: The closing price and percent change of IDTC over the last 5 days

Day:	FRI	MON	TUE	WED	THU
Close	25.9375	26.375	29.5	28.75	28.0625
Change ($\Delta x$)	-	0.4375	3.125	-0.75	-0.6875
% Change ( $100\times (\Delta x)/x$)	-	1.69	11.85	-2.54	-2.39