Calculating a Percent Gain

You bought shares for 80 dollars and sold them for 100 dollars. What is your percent gain?

Identify the values: Original value = 80 dollars, New value = 100 dollars = Values identified

Find the change: $100 - 80 = 20$ dollars profit = Change = 20 dollars

Divide by original: $\frac{20}{80} = 0.25$ = Decimal = 0.25

Convert to percent: $0.25 \times 100\% = 25\%$ = 25% gain

Answer: You made a 25% gain on your investment.

Calculating a Percent Loss

A stock drops from 50 dollars to 35 dollars. What is the percent loss?

Identify the values: Original = 50 dollars, New = 35 dollars = Values identified

Find the change: $35 - 50 = -15$ dollars = Change = -15 dollars

Divide by original: $\frac{-15}{50} = -0.30$ = Decimal = -0.30

Convert to percent: $-0.30 \times 100\% = -30\%$ = 30% loss

Answer: The stock lost 30% of its value.

The Recovery Trap

Your investment loses 50%. How much must it gain to get back to the original value?

Start with an example: Imagine you start with 100 dollars = Original = 100 dollars

Calculate 50% loss: $100 - 50\% = 100 - 50 = 50$ dollars = After loss: 50 dollars

Find needed gain: You need to go from 50 back to 100 dollars = Need +50 dollars

Calculate percent gain needed: $\frac{50}{50} \times 100\% = 100\%$ = Need 100% gain!

Answer: After a 50% loss, you need a 100% gain to break even. This is why losses hurt more than gains of the same percentage!

Mistake: Using the new value as the denominator

Why: Percent change is always relative to the ORIGINAL (starting) value, not the new value.

Correct: Always divide by the original value: $\frac{\text{New} - \text{Original}}{\text{Original}}$

Mistake: Thinking a 50% loss and 50% gain cancel out

Why: After a 50% loss, you have half your money. A 50% gain on half is only 75% of original.

Correct: 100 dollars - 50% = 50 dollars. Then 50 dollars + 50% = 75 dollars. You still lost 25%!

Mistake: Forgetting to multiply by 100

Why: The formula gives a decimal. You must multiply by 100 to get a percentage.

Correct: $0.25$ is not 25%. You must write $0.25 \times 100\% = 25\%$

Stock Market Returns

Investors track percent gains and losses to evaluate their portfolio performance.

If you invested 1000 dollars and your portfolio is now worth 1150 dollars, you have a $\frac{1150-1000}{1000} \times 100\% = 15\%$ gain.

Comparing Investment Options

Percent change helps compare investments of different sizes.

Investment A: 500 dollars becomes 600 dollars (20% gain). Investment B: 2000 dollars becomes 2300 dollars (15% gain). Investment A performed better even though B earned more dollars.

Q: Why do I divide by the original value and not the new value?

A: Percent change measures how much the value changed relative to where it started. The original value is your reference point. If you used the new value, you'd be measuring something different.

Q: What's the difference between percent gain and total return?

A: Percent gain is the percentage increase in value. Total return includes percent gain plus any dividends or interest earned during the holding period.

Q: Can you have more than 100% gain?

A: Yes! If an investment doubles, that's 100% gain. If it triples, that's 200% gain. There's no upper limit to gains, but losses are capped at 100% (losing everything).