Math Problem Statement

You bought a stock for ​$42.42​, and you sold it one year later for ​$44.98.
It paid a dividend of ​$1.73 three months after you purchased it. It paid a second dividend of ​$1.81 nine months after you purchased it. What was your return on the stock over that time​ period?

Solution

To calculate the total return on the stock, we need to account for both the capital gain (or loss) and the dividend income. Here's how we can break it down:

1. Capital Gain (or Loss):

Capital gain is the difference between the selling price and the purchase price.

Capital Gain=Selling PricePurchase Price\text{Capital Gain} = \text{Selling Price} - \text{Purchase Price} Capital Gain=44.9842.42=2.56\text{Capital Gain} = 44.98 - 42.42 = 2.56

2. Dividend Income:

The total dividend income is the sum of the two dividends received during the year.

Total Dividends=First Dividend+Second Dividend\text{Total Dividends} = \text{First Dividend} + \text{Second Dividend} Total Dividends=1.73+1.81=3.54\text{Total Dividends} = 1.73 + 1.81 = 3.54

3. Total Return:

The total return is the sum of the capital gain and the dividend income, divided by the initial purchase price.

Total Return=Capital Gain+Total DividendsPurchase Price\text{Total Return} = \frac{\text{Capital Gain} + \text{Total Dividends}}{\text{Purchase Price}} Total Return=2.56+3.5442.42=6.1042.420.143\text{Total Return} = \frac{2.56 + 3.54}{42.42} = \frac{6.10}{42.42} \approx 0.143

So, the total return on the stock over the year is approximately 14.3%.

Summary:

  • Capital gain: $2.56
  • Dividend income: $3.54
  • Total return: 14.3%

Would you like further clarification on any part of this calculation?

Here are some related questions:

  1. How do you calculate the return on a stock if you receive dividends periodically?
  2. How does the time at which dividends are paid affect the total return?
  3. What is the difference between total return and price return?
  4. How do capital gains taxes impact your overall return on a stock?
  5. How does reinvesting dividends affect total return over time?

Tip: When calculating returns, always consider both the price change and dividends, as they together contribute to the overall profitability of the investment.

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Math Problem Analysis

Mathematical Concepts

Investment Returns
Percentage Calculation
Capital Gains
Dividend Income

Formulas

Capital Gain = Selling Price - Purchase Price
Total Dividends = First Dividend + Second Dividend
Total Return = (Capital Gain + Total Dividends) / Purchase Price

Theorems

Basic Percentage Calculation
Investment Return Formula

Suitable Grade Level

High School (Grades 10-12), College Finance Courses