8. You invested $2,000 in the stock market one year ago. Today, the investment is valued at $9,500. What return did you earn? What return would you need to suffer next year for your investment to be valued at the original $2,000?

a. P = Po + Po*r*t = $9,500

2,000 + 2000*r*1 = 9,500
Solve for r.

b. 9500 - 9500*r*t = 2000
9500 - 9500*r*1 = 2000
-9500r = 2000-9500 = -7500
r = 0.7895 = 78.95%

To calculate the return on investment (ROI), you can use the following formula:

ROI = (Current Value - Initial Investment) / Initial Investment * 100

In this case, your initial investment was $2,000, and the current value of your investment is $9,500.

ROI = (9500 - 2000) / 2000 * 100
ROI = 7.75 * 100
ROI = 775%

So, the return you earned on your investment is 775%.

To find out what return you would need to suffer next year for your investment to be valued at the original $2,000, you need to solve for ROI in the formula using the original investment value as the current value, and $2,000 as the future value.

ROI = (Future Value - Current Value) / Current Value * 100

Let's assume the future value is $2,000. We need to find the ROI.

2000 = (2000 - 9500) / 9500 * 100

Simplifying the equation:

2000 = -7500 / 9500 * 100

2000 = -78.95

Since it is not possible for ROI to be negative, it is not possible for your investment to be valued at the original $2,000 next year.