$7.$ You are considering the choice between investing $75000$ USD in a conventional $1-$year bank CS offering an interest rate of $5\%$ and a $1-$year $$inflation$-$plus$$ CS offering $1\mathrm{.}5\%$ per year plus the rate of inflation.

$7$a Which is the safer investment?

$7$b Which offers the higher expected return?

$7$c If you expect the rate of inflation to be $3\%$ over the next year, which is the better investment? Why?

$7$d If we observe a risk$-$free nominal interest rate of $5\%$ per year and a risk$-$free real rate of $1\mathrm{.}5\%$ on inflation$-$ indexed bonds, can we infer that the market$$s expected rate of inflation is $3\mathrm{.}5\%$ per year?