Calvin invested in shares of four different companies at the beginning of the year. At the end of the year the share values had increased or decreased as follows:


WestCo

Runners

DigiCom

SouthCo

-2.91%8.23%-4.49%9.50%

For full marks your answers should be given as percents accurate to at least two decimal places.


What is the total rate of return if Calvin invests the same amount in each company?

 Return = 0.00%




What is the total rate of return if Calvin invests three times as much in Runners as in the other companies?

 Return = 0.00%





To find the total rate of return, we'll calculate it under two scenarios: when Calvin invests the same amount in each company and when he invests three times as much in Runners as in the other companies.

### 1. Equal Investment in Each Company

If Calvin invests the same amount in each company, the total rate of return is simply the average of the returns from all four companies.

Given:
- WestCo: \(-2.91\%\)
- Runners: \(8.23\%\)
- DigiCom: \(-4.49\%\)
- SouthCo: \(9.50\%\)

The total rate of return is:

\[
\text{Total Rate of Return} = \frac{(-2.91) + 8.23 + (-4.49) + 9.50}{4}
\]

Now, let's calculate:

\[
\text{Total Rate of Return} = \frac{-2.91 + 8.23 - 4.49 + 9.50}{4} = \frac{10.33}{4} = 2.5825\%
\]

So, the total rate of return when Calvin invests the same amount in each company is **2.58%**.

### 2. Investing Three Times as Much in Runners

In this case, Calvin's investment in Runners is three times as much as in the other companies. The weighted average formula applies here:

\[
\text{Total Rate of Return} = \frac{1(-2.91) + 3(8.23) + 1(-4.49) + 1(9.50)}{1 + 3 + 1 + 1}
\]

Calculate the total rate of return:

\[
\text{Total Rate of Return} = \frac{-2.91 + 24.69 - 4.49 + 9.50}{6} = \frac{26.79}{6} = 4.465\%
\]

So, the total rate of return when Calvin invests three times as much in Runners is **4.47%**.

Would you like further clarification or additional details?

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Here are 5 related questions you might find interesting:
1. How would the total rate of return change if Calvin invested twice as much in SouthCo instead of Runners?
2. What would the rate of return be if DigiCom had a return of 0% instead of -4.49%?
3. If Calvin wants a target rate of return of 5%, how should he adjust his investments in these companies?
4. How would the total rate of return change if all investments had the same positive return?
5. What is the impact on the total rate of return if WestCo's return becomes positive?

**Tip:** When dealing with multiple investments, it's crucial to understand how different weights or amounts invested affect the overall return. This can help in making more informed financial decisions.

Learn how to calculate the total rate of return when investing in multiple companies with different returns. Solve scenarios where equal investment is made in each company and when one company receives three times more investment than others. Includes detailed formulas and step-by-step solutions.

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