You are considering the choice between investing $$100,000$ in a conventional $1-$year bank certificate of deposit offering an interest rate of $6\%$ and a $1-$year inflation protected certificate of deposit offering $3\%$ per year plus the rate of inflation.a$.$ Which is the safer investment in terms of purchasing power?b$.$ Can you tell which offers the higher expected return?c$.$ If you expect the rate of inflation to be $2\%$ over the next year, which is the better investment? Why?