Real and nominal rates interest Zane Perelli currently has $$108$ that he can spend today on socks costing $$2\mathrm{.}70$ each. Alternatively, he could invest the $$108$ in a risk$-$free U$.$S$.$ Treasury

security that is expected to earn a $13\%$ nominal rate of interest. The consensus forecast of leading economists is a $5\%$ rate of inflation over the coming year.

a$.$ How many socks can Zane purchase today?

b$.$ How much money will Zane have at the end of $1$ year if he forgoes purchasing the socks today and invests his money instead? $($Ignore taxes.$)$

c$.$ How much would you expect the socks to cost at the end of $1$ year in light of the expected inflation?

d$.$ Use your findings in parts $b$ and $c$ to determine how many socks $($fractions are OK$)$ Zane can purchase at the end of $1$ year. In percentage terms, how many more or fewer socks can Zane

buy at the end of $1$ year?

e$.$ What is Zane's approximate real rate of return over the year? How is it related to the percentage change in Zane's buying power found in part d$?$ Explain.

a$.$ The number of socks Zane can purchase today is socks. $($Round to the nearest whole number.$)$