You are considering investing $$1,000$ in a T$-$bill that pays $0\mathrm{.}05$ and a risky portfolio, P$,$

constructed with two risky securities$,$ X and Y$.$ The weights of X and Y in P are $0\mathrm{.}60$ and $0\mathrm{.}40,$

respectively. X has an expected rate of return of $0\mathrm{.}14$ and variance of $0\mathrm{.}01,$ and Y has an expected

rate of return of $0\mathrm{.}10$ and a variance of $0\mathrm{.}0081.$

If you want to form a portfolio with an expected rate of return of $0\mathrm{.}10,$ what percentages of your

money must you invest in the T$-$bill, X$,$ and Y$,$ respectively, if you keep X and Y in the same

proportions to each other as in portfolio P$?$

A$)0\mathrm{.}32$; $0\mathrm{.}41$; $0\mathrm{.}27$

B$)0\mathrm{.}19$; $0\mathrm{.}49$; $0\mathrm{.}32$

C$)0\mathrm{.}50$; $0\mathrm{.}30$; $0\mathrm{.}20$

D$)$ Cannot be determined.

E$)0\mathrm{.}25$; $0\mathrm{.}45$; $0\mathrm{.}30$