https://file.aiquickdraw.com/mathbot/file/1729642208984vapyy2kx.jpg

Let's break down the problem:

The investor owns stocks in two companies:
1. **Company A**: Initial value was \$6120. The stock increased by 5% over the past year.
2. **Company B**: Initial value was \$1920. The stock increased by 20% over the past year.

We need to calculate the total percentage increase in the value of the investor's stock portfolio.

### Step 1: Calculate the new values of the stocks after their respective percentage increases.

- For **Company A**:
  \[
  \text{New Value of Company A's stock} = 6120 + 6120 \times \frac{5}{100} = 6120 + 306 = 6426
  \]

- For **Company B**:
  \[
  \text{New Value of Company B's stock} = 1920 + 1920 \times \frac{20}{100} = 1920 + 384 = 2304
  \]

### Step 2: Calculate the total initial value and total new value.

- **Initial total value**:
  \[
  6120 + 1920 = 8040
  \]
- **New total value**:
  \[
  6426 + 2304 = 8730
  \]

### Step 3: Calculate the total percentage increase.
\[
\text{Percentage increase} = \left(\frac{\text{New Total Value} - \text{Initial Total Value}}{\text{Initial Total Value}}\right) \times 100 = \left(\frac{8730 - 8040}{8040}\right) \times 100 = \left(\frac{690}{8040}\right) \times 100 \approx 8.58\%
\]

Thus, the total percentage increase in the investor's stock account is approximately **8.6%**.

Would you like a more detailed explanation or have any other questions?

Here are five related questions to expand on this topic:
1. How would the calculation change if the stock in Company A decreased by 5% instead of increasing?
2. What would be the total percentage increase if both stocks increased by the same percentage?
3. How would you calculate the weighted average return if the investor had different amounts invested in each company?
4. How do you calculate the percentage decrease if the stock values had fallen?
5. Can you use this same method to calculate percentage increases for a portfolio with more than two companies?

**Tip**: Always make sure to calculate percentage changes for each stock separately, especially when they experience different growth rates.

An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $6120, and his stock in Company B was worth $1920. The stock in Company A has increased 5% since last year, and the stock in Company B has increased 20%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth.

Learn how to calculate the total percentage increase for an investor's stock account. The problem covers percentage increases for two stocks: Company A's stock grew 5%, and Company B's stock grew 20%. Find the overall percentage increase by calculating the new values and determining the change in total stock value.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation