Math Problem Statement

You bought a share of 2 percent preferred stock for $96.93 last year. The market price for your stock is now $98.85.    What was your total return for last year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)  

Solution

To calculate the total return for the preferred stock, we need to consider both the income (dividend) and the capital gain (or loss) from the change in the stock price.

Steps:

  1. Dividend Income: Since the preferred stock pays a 2% dividend, we can calculate the dividend based on the original purchase price: Dividend Income=Purchase Price×Dividend Rate\text{Dividend Income} = \text{Purchase Price} \times \text{Dividend Rate} Dividend Income=96.93×0.02=1.9386\text{Dividend Income} = 96.93 \times 0.02 = 1.9386

  2. Capital Gain: The change in stock price is the difference between the current market price and the purchase price: Capital Gain=Market PricePurchase Price\text{Capital Gain} = \text{Market Price} - \text{Purchase Price} Capital Gain=98.8596.93=1.92\text{Capital Gain} = 98.85 - 96.93 = 1.92

  3. Total Return: The total return is the sum of the dividend income and the capital gain, divided by the purchase price, then multiplied by 100 to get the percentage: Total Return=(Dividend Income+Capital GainPurchase Price)×100\text{Total Return} = \left( \frac{\text{Dividend Income} + \text{Capital Gain}}{\text{Purchase Price}} \right) \times 100 Total Return=(1.9386+1.9296.93)×100=(3.858696.93)×100\text{Total Return} = \left( \frac{1.9386 + 1.92}{96.93} \right) \times 100 = \left( \frac{3.8586}{96.93} \right) \times 100 Total Return3.98%\text{Total Return} \approx 3.98\%

Answer:

Your total return for last year was 3.98%.


Would you like more details on any part of the calculation, or do you have other questions?

Here are some related questions you might find helpful:

  1. How do dividends affect total return versus stock price changes?
  2. What is the difference between capital gains and dividend income in terms of taxation?
  3. How would total return change if the stock price had decreased instead of increased?
  4. What factors influence the price of preferred stock?
  5. How do market conditions affect preferred stock prices?

Tip: When calculating total return, always consider both the dividends and capital gains/losses for a comprehensive view.

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Math Problem Analysis

Mathematical Concepts

Finance
Percentage Calculation
Dividend and Capital Gains

Formulas

Dividend Income = Purchase Price × Dividend Rate
Capital Gain = Market Price - Purchase Price
Total Return = ((Dividend Income + Capital Gain) / Purchase Price) × 100

Theorems

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Suitable Grade Level

Grades 11-12