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Let's break down this problem step by step:

1. **Initial Investment:** You start with \$13,000.
2. **First Year:** Your investment decreases by 30%. So, the value at the end of the first year is:
   \[
   13,000 \times (1 - 0.30) = 13,000 \times 0.70 = 9,100
   \]
   After the first year, the investment is worth \$9,100.
   
3. **Second Year:** The investment increases by 40% in the second year. So, the value at the end of the second year is:
   \[
   9,100 \times (1 + 0.40) = 9,100 \times 1.40 = 12,740
   \]
   After the second year, the investment is worth \$12,740.

4. **Overall Percent Change:** Now, let's calculate the overall percent change from the original \$13,000 to \$12,740. The formula for percent change is:
   \[
   \text{Percent Change} = \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \times 100
   \]
   Substituting the values:
   \[
   \frac{12,740 - 13,000}{13,000} \times 100 = \frac{-260}{13,000} \times 100 \approx -2\%
   \]
   So, there is an overall **2% loss**.

### Answer:
- The financial advisor is **incorrect** in saying there was a 10% overall increase. In fact, there was a **2% overall loss**.
- The correct answer is **D: No, there is an actual percent loss of 2%.**

Do you need any more details on this calculation?

### Follow-up questions:
1. How would the outcome change if the second year increase was 50% instead of 40%?
2. What would be the overall change if the first year's decrease was 20% instead of 30%?
3. How would a 10% gain in the first year and a 30% loss in the second year affect the overall investment?
4. What if the decrease and increase were calculated with different initial investments, say \$10,000?
5. How do percentages compound over multiple periods? Would using simple vs. compound percentage change the results?

**Tip:** When dealing with multiple percentage changes, always apply each change sequentially to the new value, not the original amount.

Suppose that you have $13,000 in a rather risky investment recommended by your financial advisor. During the first year, your investment decreases by 30% of its original value. During the second year, your investment at the end of year one increases by 40%. Your advisor tells you there must have been a 10% overall increase of your original $13,000 investment. Is your financial advisor using percentages properly? If not, what is your actual percent gain or loss of your original $13,000 investment?

Learn how to calculate the overall percentage gain or loss on a $13,000 investment that decreases by 30% in the first year and increases by 40% in the second year. This step-by-step solution covers the application of percentage changes over multiple periods.

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