$3.$ You have a choice of investing in two government notes with a $5-$year maturity and a $$10,000$ face value. The first pays $6\mathrm{.}8\%$ annually. The second pays a real yield of $4\mathrm{.}0\%$ with the amount of interest adjusted annually based on changes in the CPI $($the CPI was at $100$ when the notes were issued$).$ See the table below for the CPI in each year.

a$.$ How much interest is paid each year on each security?

b$.$ Using the dollar$-$weighted return $($see CH $10),$ what is the nominal, annual rate of return on each security?

c$.$ Based on the answer to $($b$),$ which alternative produced the higher return, and why?