Question

Over the last four months, your investment lost

10%, 20%, 30%, and then 40%. What percent
of the original investment do you have left?

Answer 1

30.24%

Explanation:

Each time you lose x%, you end up with 1 - 0.01x.

For example, if you lose 10% of an amount, you end up with 1 - 0.01(10), or 0.9 times the original amount.

Let's say you started with x.

You lost 10%. Now you have 0.9x.

Then you lost 20% of the remaining amount. Now you have 0.8(0.9x).

Then you lost 30% of the remaining amount. Now you have 0.7(0.8)(0.9x).

Finally you lost 40% of the remaining amount. Now you have 0.6(0.7)(0.8)(0.9x).

The final amount you have is

0.6(0.7)(0.8)(0.9x) = 0.3024x = 30.24% of x

Answer: 30.24%