Question

Suppose that you have ​$12,000 in a rather risky investment recommended by your financial advisor. During the first​ year, your investment decreases by 50​% of its original value. During the second​ year, your investment at the end of year one increases by 60​%. Your advisor tells you that there must have been a 10​% overall increase of your original ​$12,000 investment. Is your financial advisor using percentages​ properly? If​ not, what is your actual percent gain or loss of your original ​$12,000 ​investment?

Answer 1

20% loss

Explanation:

If the investment decreases by 50% during the first year, then it is 50% of its original value at the end of the first year, since 100% - 50% = 50%.

Calculate 50% of $12,000:

`\implies (50)/(100) * 12000 = 6000`

Therefore, the value of investment at the end of the first year is $6,000.

If the investment increases by 60% during the second year, then it is 160% of its value at the end of year one, since 100% + 60% = 160%.

Calculate 160% of $6,000:

`\implies (160)/(100) * 6000=9600`

Therefore, there has been a net loss since $9,600 is less than the original investment.

Percent Change

`\sf Percent\:change=(final\:value-initial\:value)/(initial\:value) * 100`

To calculate the actual percent loss of the original investment, use the percent change formula:

`\implies \textsf{Percent change}=(9600-12000)/(12000) * 100=-20\%`

As the percent change is negative, this represents a loss.

Therefore, the actual percent loss of the original $12,000 investment is 20%.