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?
To calculate the return you earned on your investment, use the formula:
Return = (Final Value - Initial Value) / Initial Value
In this case, the initial value is $2,000 and the final value is $9,500. Plugging these values into the formula:
Return = ($9,500 - $2,000) / $2,000 = 3.75
So, you earned a return of 3.75 or 375%.
Now, to calculate the return you would need to suffer next year for your investment to be valued at the original $2,000, you can rearrange the formula:
Return = (Final Value - Initial Value) / Initial Value
To solve for the Final Value:
Final Value = (Return * Initial Value) + Initial Value
In this case, since you want the final value to be $2,000 and the initial value is $9,500, plug these values into the formula and solve for the return:
$2,000 = (Return * $9,500) + $9,500
Subtracting $9,500 from both sides:
$2,000 - $9,500 = Return * $9,500
Simplifying:
-$7,500 = Return * $9,500
Dividing both sides by $9,500:
Return = -0.7895
So, for your investment to be valued at the original $2,000 next year, you would need to suffer a negative return of -0.7895 or -78.95%.