Suppose there is a simple index of three stocks, stock x, stock y, and stock z. stock x opens the day with 2000 shares at $3.80 per share. stock y opens the day with 1000 shares at $3.50 per share. stock z opens the day with 3000 shares at $4.30 per share. this simple index rises 5.4% over the course of the day. what is the value of the index at the end of the day? round your answer to the nearest hundred

This is a question written by someone who doesn't know much about finance.  We wouldn't usually talk about shares of an index member, but perhaps the weight of each member in an index, i.e. a cap weighting or a price weighting.  We would talk about shares of stock in a portfolio; let's substitute portfolio for index and interpret the question that way.

We'd also usually talk about the change in the stock prices from the close of the previous day, not usually from today's open. OK, enough correcting the question.

So at the open we're long 2000 X @ 3.80, 1000 Y @ 3.50 and 3000 Z @ 4.30.  The value of this portfolio at the open is



At the end of the day we're told we've made 5.4% so our portfolio is valued at



5.4% is what pros call a good day.