Kate purchased a share of a stock for 99. After six months, the price of the stock was 112 and the stock paid a dividend of 7. One year after purchase, the price of the stock was 116 and the stock paid a dividend of 5. Calculate the total annual return on Kate's investment. Provide your answer as an annual effective rate.


To calculate the total annual return on Kate's investment, we need to determine how much profit she made over the course of the year (including both the change in the stock price and the dividends) and express that as a percentage of the original purchase price. Then, we'll convert that into an annual effective rate.

### Step-by-Step Calculation:

#### 1. **Initial Purchase Price**:
Kate bought the stock for \( P_0 = 99 \).

#### 2. **Price and Dividend at 6 months**:
- After 6 months, the stock price was \( P_{6m} = 112 \).
- A dividend of \( D_{6m} = 7 \) was paid at that time.

#### 3. **Price and Dividend after 1 year**:
- After 12 months (1 year), the stock price was \( P_{1y} = 116 \).
- A dividend of \( D_{1y} = 5 \) was paid at that time.

#### 4. **Total Return (Profit)**:
- The price change after one year is:  
  \( P_{1y} - P_0 = 116 - 99 = 17 \).
- Total dividends received during the year:  
  \( D_{6m} + D_{1y} = 7 + 5 = 12 \).
- Total profit (capital gain + dividends) is:  
  \( 17 + 12 = 29 \).

#### 5. **Rate of Return**:
- The total return over one year is the profit as a percentage of the initial purchase price:
  \[
  \text{Total return} = \frac{29}{99} = 0.2929 \approx 29.29\%
  \]

Thus, the total annual return on Kate's investment is approximately **29.29%**, expressed as an annual effective rate.

Would you like any further details or clarifications?

### Related Questions:
1. How would the annual return change if dividends were reinvested?
2. Can the return be considered in terms of compounded growth over shorter intervals?
3. How would transaction fees affect the total annual return?
4. What if the dividend payments were at different time intervals?
5. How do you calculate annualized returns if the investment period is less than a year?

#### Tip:
When calculating investment returns, always consider both the price appreciation and any income received, such as dividends, to get the full picture of your total return.

Kate purchased a share of a stock for 99. After six months, the price of the stock was 112 and the stock paid a dividend of 7. One year after purchase, the price of the stock was 116 and the stock paid a dividend of 5. Calculate the total annual return on Kate's investment. Provide your answer as an annual effective rate.

Learn how to calculate the total annual return on an investment in stocks, considering both price appreciation and dividends. This detailed solution explains how to find the total return and express it as an annual effective rate. Suitable for advanced high school and college-level students.

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