Mr. Jackson invests an amount of money in such a way that if the stock goes up for 6 months, he doubles his money, but if it goes down for 1 month he loses 2/3 of it. If it goes up 6 months, then down one month, then down another month, then up 6 months, down 1 month and up 6 months, what fractional part of his money is left?
Assuming Mr. Jackson starts with $1, we can track how his investment changes over time.
After 6 months of growth, his investment doubles to $2.
Then, he loses 2/3 of $2, which is $4/3. His investment is now worth $2 - $4/3 = $2/3.
After another month of decline, his investment is further reduced by 2/3, leaving him with $2/3 - $4/9 = $2/9.
Over the next 6 months of growth, his investment doubles again to $4/9 * 2 = $8/9.
Then, he loses 2/3 of $8/9, which is $16/27. His investment is now worth $8/9 - $16/27 = $4/27.
Finally, another 6 months of growth doubles his remaining investment to $4/27 * 2 = $8/27.
Therefore, the fractional part of his money that is left is $8/27, or approximately 0.30.