Problem 71 - Introductory Algebra for College Students

Question

Suppose that you put \(\$ 10,000\) 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 increases by \(40 \%\) of its first-year value. Your advisor tells you that there must have been a \(10 \%\) overall increase of your original \(\$ 10,000\) investment. Is your financial advisor using percentages properly? If not, what is the actual percent gain or loss on your original \(\$ 10,000\) investment?

Step-by-Step Solution

Answer

No, the financial advisor is not using percentages properly. There is actually a 2% overall decrease in the original $10,000 investment, not a 10% increase.

Step 1: Calculate the Value After the First Year

In the first year the investment decreases by 30%. So, if the initial investment is \( p \), the amount after the first year is \( p - (0.3 \times p) = 0.7 \times p \). Substituting the value of \( p \) being $10,000; after the first year, the investment will be \( 0.7 \times 10,000 = \$7,000\).

Step 2: Calculate the Value After the Second Year

In the second year, the investment increases by 40% of its reduced value. So, if the amount after the first year is \( p1 \), the amount after the second year would be \( p1 + (0.4 \times p1) = 1.4 \times p1 \). Substituting the value of \( p1 \) being \$7,000, after the second year, the investment would be \( 1.4 \times 7,000 = \$9,800\).

Step 3: Calculate the Overall Percentage Change

The overall percent change can be calculated by subtracting the original investment from the final value, dividing by the original investment, and then multiplying by 100 to get a percentage. This will give: \( ((9800 - 10000) / 10000) \times 100 = -2\% \). So, the investment has actually decreased by 2% over the two years period.