Question

Suppose that you invest $10,000 in a risky investment. at the end of the first year, the investment has decreased by 50% of its original value. at the end of the second year, the investment increases by 60% of the value it had at the end of the first year. your investment consultant tells you that there must have been a 10% overall increase of the original $10,000 investment. is this an accurate statement? if not, what is your actual percent gain or loss on the original $10,000 investment. round to the nearest percent.

Answer 1

well, let's take a looksie, if it decreased by 50% the 1st year, that means what's leftover is 50% of it, well

`\begin{array}c \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{50\% of 10000}}{\left( \cfrac{50}{100} \right)10000}\implies 5000`

so, on the next year it increases by 60% of 5000

`\begin{array}c \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{60\% of 5000}}{\left( \cfrac{60}{100} \right)5000}\implies 3000~\hfill \underset{current~value}{\stackrel{5000~~ + ~~3000}{8000}}`

well, 10% of 10000 is 1000 bucks, if the consultant is correct, I should have 10000 + 1000 = 11000, but I don't, so he needs a nice cup of tea and chill some.

well, I started with 10000 bucks, now I only have 8000, lost 2000 bucks, 2000 is 1/5 of 10000 or namely 20%.