Assume that you can invest $1,000 in a savings account or a fund consisting of different stocks. If you invest in the savings account, you get 1% interest per year. The fund has annual return X with expected value E(X) = 6% and standard deviation (X) = 20%. This means that, compared to the savings account, the fund has a higher return on average, but also comes with risk. When you invest y dollars in the fund, you will have y(1 + X) dollars after one year.

(a) If you invest $500 in each the savings account and the fund, what is the expected value of the total investment that you will have after one year?

b) Assume that you choose your investment such that the expected value of the return is 4% over one year. How much do you invest of the $1,000 in the fund and the savings account? Hint: set y equal to the investment in the fund and write an equation for y using that in general, return = (terminal valueinitial value) /initial value .

(c) Assume that you choose your investment such that the standard deviation of the return is 15% over one year. How much do you invest of the $1,000 in the fund and the savings account? Your investments in the fund and savings account should be positive amounts.