I've got a homework question which I think I have solved but am not certain if the answers are correct. The question goes like this: Consider a stock which has a 50% chance of increasing by 80% by the end of the week and a 50% chance of decreasing by 60% after a week. The initial investment amount is 10000.
a) What is the expected value of the investment after 52 weeks?
I used a binomial model for the stock price so that the expected value is 10000*(0.5*1.8 + 0.5*0.4)^{52}. Is this correct?
b) What is the most likely value your investment will be?
Based on the binomial model again, the value of the investment at the end of 52 weeks can be written as V(52) = 10000 *1.8^X *0.4^{n-X}$, where $X \sim bin(n,p)$, $n=52$ and $p=0.5$. In this case, is the most likely value found using the mean of $X$; i.e, $np=26$? In other words, my solution is $V(52) = 10000 *1.8^{26} *0.4^{52-26}$.
Would appreciate any advice and/or comments on whether this is the correct way to solve the problem. Thanks!