Calculating Simple Return

Sarah invested 500 dollars in a stock. After one year, her investment is worth 575 dollars. What is her percentage return?

Identify the values: Initial Investment = 500 dollars, Final Value = 575 dollars = Values identified

Calculate total return: Total Return = 575 - 500 = 75 dollars = 75 dollars gained

Calculate percentage return: $\frac{75}{500} \times 100\%$ = $0.15 \times 100\% = 15\%$

Interpret the result: Sarah earned 15% on her investment = 15% return

Answer: Sarah earned a 15% return on her investment.

Return with a Loss

Marcus bought shares for 800 dollars. The value dropped to 680 dollars. What is his percentage return?

Identify the values: Initial = 800 dollars, Final = 680 dollars = Values identified

Calculate total return: Total Return = 680 - 800 = -120 dollars = Loss of 120 dollars

Calculate percentage return: $\frac{-120}{800} \times 100\%$ = $-0.15 \times 100\% = -15\%$

Interpret the result: Negative return means a loss = -15% return (loss)

Answer: Marcus had a -15% return, meaning he lost 15% of his investment.

Comparing Two Investments

Investment A: 200 dollars grew to 250 dollars. Investment B: 1,000 dollars grew to 1,100 dollars. Which had the better return?

Calculate Investment A return: $\frac{250 - 200}{200} \times 100\% = \frac{50}{200} \times 100\%$ = 25% return

Calculate Investment B return: $\frac{1100 - 1000}{1000} \times 100\% = \frac{100}{1000} \times 100\%$ = 10% return

Compare percentages: 25% > 10% = Investment A performed better

Note the insight: Even though B gained more dollars (100 vs 50), A had better percentage growth = Percentage matters!

Answer: Investment A had a 25% return vs Investment B's 10% return. Investment A performed better.

Annualized Return

An investment of 1,000 dollars grew to 1,331 dollars over 3 years. What is the annualized (yearly) return?

Calculate total return: Total Return = $\frac{1331 - 1000}{1000} = 33.1\%$ over 3 years = 33.1% total

Use the annualized formula: Annualized Return = $\left(\frac{\text{Final}}{\text{Initial}}\right)^{1/n} - 1$ = Formula setup

Substitute values: $\left(\frac{1331}{1000}\right)^{1/3} - 1 = (1.331)^{0.333} - 1$ = $(1.331)^{1/3}$

Calculate: $1.10 - 1 = 0.10 = 10\%$ = 10% per year

Answer: The annualized return is 10% per year. This means the investment grew at an average rate of 10% each year.

Mistake: Using dollar amount to compare investments instead of percentage

Why: A 100-dollar gain means different things for different investment sizes. On a 1,000-dollar investment it's 10%, but on a 10,000-dollar investment it's only 1%.

Correct: Always calculate percentage return to fairly compare investments of different sizes.

Mistake: Forgetting that returns can be negative

Why: When the final value is less than the initial investment, you have a loss (negative return).

Correct: If Final Value < Initial Investment, your return is negative. This is normal and important to track.

Mistake: Confusing total return with annualized return

Why: A 30% return over 3 years is NOT the same as 30% per year. The annualized return is about 9.1%.

Correct: Use the annualized formula for multi-year investments: $(\text{Final}/\text{Initial})^{1/n} - 1$

Stock Market Investing

Investors use percentage returns to evaluate stock performance and compare different companies.

If Apple stock goes from 150 dollars to 180 dollars per share, the return is $\frac{30}{150} \times 100\% = 20\%$.

Savings Account Interest

Banks advertise interest rates, but calculating your actual return helps you understand how much you will earn.

A savings account with 2,000 dollars earns 3% annual interest. Return = 2000 * 0.03 = 60 dollars.

Real Estate Investment

Property investors calculate returns to decide whether buying rental property or other investments makes more sense.

A house bought for 200,000 dollars and sold for 250,000 dollars gives a return of $\frac{50000}{200000} \times 100\% = 25\%$.

Q: What is a good investment return?

A: It depends on the investment type. Historically, the stock market averages about 7-10% per year. Savings accounts offer 1-5%. Higher returns usually mean higher risk.

Q: Can returns be more than 100%?

A: Yes! If an investment doubles, that is a 100% return. If it triples, that is a 200% return. However, you can never lose more than 100% (your entire investment).

Q: Why do we use percentage instead of dollar amounts?

A: Percentage lets you compare investments fairly. Earning 100 dollars on a 500-dollar investment (20%) is better than earning 100 dollars on a 5,000-dollar investment (2%).