https://file.aiquickdraw.com/mathbot/file/1726594241971g3ridm8w.jpg

The problem involves inverse mutual funds where the user has invested a total of $15,000 in three funds, and the year-to-date losses are given for each fund. The goal is to determine how much the user invested in each of the three funds given that the losses from the first two funds (SHPIX and RYURX) total $400, and RYURX and RYCWX have equal investments.

### Information provided:
1. **Total investment** = $15,000.
2. **Loss from SHPIX** = 4%.
3. **Loss from RYURX** = 3%.
4. **Loss from RYCWX** = 6%.
5. **Total loss from SHPIX and RYURX** = $400.
6. Investments in **RYURX** and **RYCWX** are equal.

### Step-by-step solution:

Let:
- The investment in **SHPIX** = $ x $.
- The investment in **RYURX** = $ y $.
- The investment in **RYCWX** = $ y $ (since the investments in RYURX and RYCWX are equal).

From the total investment:
\[
x + y + y = 15,000 \quad \Rightarrow \quad x + 2y = 15,000 \quad (1)
\]

The losses are calculated as follows:
- **Loss from SHPIX** = $ 0.04 \times x $.
- **Loss from RYURX** = $ 0.03 \times y $.

The total loss from SHPIX and RYURX is given as $400:
\[
0.04x + 0.03y = 400 \quad (2)
\]

Now, we have the system of two equations:
1. $ x + 2y = 15,000 $
2. $ 0.04x + 0.03y = 400 $

Let's solve this system.The solution to the system of equations gives the following investments:

- Investment in **SHPIX** = $7,000.
- Investment in **RYURX** = $4,000.
- Investment in **RYCWX** = $4,000.

These values satisfy both the total investment and the given year-to-date loss conditions.

Would you like more details or further explanation? Here are some related questions:

1. How are inverse mutual funds typically used in a portfolio?
2. What would happen if the total loss amount was higher or lower than $400?
3. How would changing the equal investment assumption between RYURX and RYCWX affect the solution?
4. What impact do these percentage losses have on long-term investments?
5. Can the year-to-date losses increase or decrease throughout the year?

**Tip:** Inverse funds are generally used for short-term strategies, and they can be risky if held for extended periods due to market volatility.

You invested a total of $15,000 in the three funds at the beginning of 2015, including an equal amount in RYURX and RYCWX. Your year-to-date loss from the first two funds amounted to $400. How much did you invest in each of the three funds?

Solve a problem where $15,000 was invested in three inverse mutual funds (SHPIX, RYURX, RYCWX). The loss from SHPIX and RYURX totals $400. Learn how to determine how much was invested in each fund using algebraic methods.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation