expected value

[cniles]

Katie just inherited $13000. Her bank has a savings account that pays 4.2% interest per year. Some of her friends recommended a new mutual fund, which has been in business for three years. During its first year, the fund went up in value by 7%; during the second year, it went down by 17%; and during its third year, it went up by 11%. Katie is attracted by the mutual fund's potential for relatively high earnings but concerned by the possibility of actually losing some of her inheritance. The bank's rate is low, but it is insured by the federal government. Use decision theory to find the best investment. (Assume that the fund's past behavior predicts its future behavior.)
I have figured out that the expected value of the bank investment is $546.00. I think that is correct, but then I am unable to figure out what the expected value of the mutual fund would be in dollars.
I got the $546 by multiplying $13000 by .042.

 

[Denis]

I have figured out that the expected value of the bank investment is $546.00.

No; that's the 1st year's interest the bank will pay on the 13000, leaving investment at 13546;
the 2nd year's interest will be 13546 * .042 = 568.93, leaving investment at 14114.93.
Calculate 3rd year similarly.

Now similarly calculate mutual fund result: use .07, then -.17, then .11

Compare results.

There are formulas for this stuff; don't think you're ready for those.