suppose that you have $9,000 in a risky investment recommended by your financial advisor. during the first…

suppose that you have $9,000 in a 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 that there must have been a 10% overall increase of your original $9,000 investment. is your financial advisor using percentages properly? if not, what is your actual percent gain or loss of your original $9,000 investment? select the correct choice below and fill in the answer boxes to complete your choice. (type a whole number.) a. no, there is an actual percent loss of % b. yes, there is an actual percent gain of % c. no, there is an actual percent gain of % d. yes, there is an actual percent loss of %

suppose that you have $9,000 in a 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 that there must have been a 10% overall increase of your original $9,000 investment. is your financial advisor using percentages properly? if not, what is your actual percent gain or loss of your original $9,000 investment? select the correct choice below and fill in the answer boxes to complete your choice. (type a whole number.) a. no, there is an actual percent loss of % b. yes, there is an actual percent gain of % c. no, there is an actual percent gain of % d. yes, there is an actual percent loss of %

Answer

Explanation:

Step1: Calculate value after first - year decrease

The initial investment is $9000$. It decreases by 30% in the first year. The value after the first - year decrease is $9000\times(1 - 0.3)=9000\times0.7 = 6300$.

Step2: Let the percentage increase in the second year be $x$.

We want the final value to be $9000\times(1 + 0.1)=9900$ (since there must be a 10% overall increase). We know the value after the first - year is 6300. So we set up the equation $6300\times(1 + x)=9900$.

Step3: Solve for $x$.

First, divide both sides of the equation $6300\times(1 + x)=9900$ by 6300: $1 + x=\frac{9900}{6300}=\frac{11}{7}\approx1.5714$. Then $x=\frac{11}{7}-1=\frac{11 - 7}{7}=\frac{4}{7}\approx0.5714$ or 57.14%.

Answer:

B. Yes, there is an actual percent gain of 57%