
Mr. A. de Dios invests his P3.5M as follows: 3/10 in time deposit, 1/3 in money market, 1/5in bonds and the rest in mutual funds. What part of his money is invested in mutual funds? Find the amount he invests in each type of investment, rounded to the nearest pesos.

To solve this problem, let's break it down step by step.

### Step 1: Determine the fraction of the investment in mutual funds.

The total fractions of Mr. A. de Dios's investment are:
- \( \frac{3}{10} \) in time deposit
- \( \frac{1}{3} \) in money market
- \( \frac{1}{5} \) in bonds

To find the fraction of the money invested in mutual funds, we need to subtract the sum of these fractions from 1 (since the total investment is 1, or 100%):

\[
\text{Fraction in mutual funds} = 1 - \left(\frac{3}{10} + \frac{1}{3} + \frac{1}{5}\right)
\]

### Step 2: Find a common denominator and sum the fractions.

The denominators are 10, 3, and 5. The least common denominator (LCD) is 30.

- Convert \( \frac{3}{10} \) to \( \frac{9}{30} \)
- Convert \( \frac{1}{3} \) to \( \frac{10}{30} \)
- Convert \( \frac{1}{5} \) to \( \frac{6}{30} \)

Now, add these fractions:

\[
\frac{9}{30} + \frac{10}{30} + \frac{6}{30} = \frac{25}{30}
\]

### Step 3: Calculate the fraction in mutual funds.

\[
\text{Fraction in mutual funds} = 1 - \frac{25}{30} = \frac{5}{30} = \frac{1}{6}
\]

### Step 4: Calculate the amount invested in each type of investment.

Mr. A. de Dios's total investment is P3.5 million (P3,500,000).

- **Time Deposit**: 
\[
\frac{3}{10} \times 3,500,000 = 1,050,000 \text{ PHP}
\]

- **Money Market**: 
\[
\frac{1}{3} \times 3,500,000 = 1,166,667 \text{ PHP}
\]

- **Bonds**: 
\[
\frac{1}{5} \times 3,500,000 = 700,000 \text{ PHP}
\]

- **Mutual Funds**: 
\[
\frac{1}{6} \times 3,500,000 = 583,333 \text{ PHP}
\]

### Final Answer:

- **Time Deposit**: P1,050,000
- **Money Market**: P1,166,667
- **Bonds**: P700,000
- **Mutual Funds**: P583,333

The fraction of his money invested in mutual funds is \( \frac{1}{6} \), and the corresponding amount is P583,333.

Would you like more details or have any other questions?

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Here are some related questions:

1. What is the importance of diversifying investments like Mr. A. de Dios did?
2. How can you calculate the return on investment (ROI) for each type of investment?
3. How would changes in interest rates affect the different types of investments mentioned?
4. What are the risks associated with investing in mutual funds compared to bonds?
5. How would Mr. A. de Dios's investments change if he decided to allocate more to mutual funds?

**Tip**: When calculating fractions, finding a common denominator is often the easiest way to sum or compare them.

Learn how to calculate fractional investments in time deposit, money market, bonds, and mutual funds with a step-by-step solution. Mr. A. de Dios invests P3.5M in various assets, and we determine the amount allocated to each investment type, rounded to the nearest peso. Suitable for Grades 7-9.

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