Math Problem Statement

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Part 1

You bought a stock one year ago for

​$50.7850.78

per share and sold it today for

​$57.7357.73

per share. It paid a

​$1.421.42

per share dividend today. What was your realized​ return?

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Part 1

The realized return was

enter your response here​%.

​(Round to two decimal​ places.)

Solution

To calculate the realized return, we need to account for both the capital gain (difference in stock price) and the dividend received during the holding period.

The formula for realized return is:

Realized Return=(Ending PriceBeginning Price+DividendBeginning Price)×100\text{Realized Return} = \left( \frac{\text{Ending Price} - \text{Beginning Price} + \text{Dividend}}{\text{Beginning Price}} \right) \times 100

Given:

  • Beginning price = $50.78
  • Ending price = $57.73
  • Dividend = $1.42

Now, let's compute the realized return:

Realized Return=(57.7350.78+1.4250.78)×100\text{Realized Return} = \left( \frac{57.73 - 50.78 + 1.42}{50.78} \right) \times 100

Realized Return=(7.95+1.4250.78)×100\text{Realized Return} = \left( \frac{7.95 + 1.42}{50.78} \right) \times 100

Realized Return=(9.3750.78)×100\text{Realized Return} = \left( \frac{9.37}{50.78} \right) \times 100

Realized Return=0.1845×100=18.45%\text{Realized Return} = 0.1845 \times 100 = 18.45\%

Final Answer:

The realized return was 18.45%.


Would you like any further details or have any questions?

Here are five related questions to explore:

  1. What would happen to the return if no dividend were paid?
  2. How would the realized return change if the ending price had been lower?
  3. What is the difference between realized and unrealized returns?
  4. How does inflation affect realized returns over time?
  5. How do you calculate annualized returns if you hold the stock for more than a year?

Tip: Always account for both price changes and dividends when calculating total stock returns!

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Math Problem Analysis

Mathematical Concepts

Investment Returns
Percentage Calculation
Dividend Yield

Formulas

Realized Return = ((Ending Price - Beginning Price + Dividend) / Beginning Price) × 100

Theorems

Basic Investment Return Formula

Suitable Grade Level

Grades 10-12