$($Portfolio expected rate of return$)$ Barry Swifter is $60$ years of age and considering retirement. Barry's retirement portfolio currently is valued at $\backslash (\backslash$$ $750,000\backslash )$ and is allocated in Treasury bills, an S$\backslash$&P $500$ index fund, and an emerging market fund as follows:

a$.$ Based on the current portfolio composition and the expected rates of return given above, what is the expected rate of return for Barry's portfolio?

b$.$ Barry is considering a reallocation of his investments to include more Treasury bills and less exposure to emerging markets. If Barry moves all of his money from the emerging market fund and puts it in Treasury bills, what will be the expected rate of return on the resulting portfolio?