Math question

Question

Suppose you invest $900 in shares of a startup company you have researched on the Internet. Unfortunately the company does not perform as well as you would have liked and you end up selling your shares 7 years later for $745 (at a loss). Compute the total and annual returns for the investment.

1)Total Return:

????% (Round to the nearest tenth of a percent, and include the negative sign in front of your answer.)

2)Annual Return:

???%(Round to the nearest tenth of a percent, and include the negative sign in front of your answer.)

Answer 1

Thank you for your question!

In order to compute the Total Return you want to take

Total Return = (Ending Value – Beginning Value) / Beginning Value * 100

So for this question that would be

($745 - $900) / $900 * 100

= -155 / 900 * 100

= -17.22%

For the Annual Return you’re after what the average yearly growth rate of the investment would be when factoring in compounding.

That is the formula

(Ending Value / Beginning Value) ^ (1 / Number of Years) – 1

=(745/900)^(1/7) – 1

=(0.8278)^(1/7) – 1

=0.9741 – 1

= -0.0259

That means that the average loss per year is around 2.59% :)