Question

 Zane Perelli currently has

​$104104

that he can spend today on socks costing

$ 2.60$2.60

each. ​ Alternatively, he could invest the

​$104104

in a​ risk-free U.S. Treasury security that is expected to earn a  

1111​%

nominal rate of interest. The consensus forecast of leading economists is a

44​%

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 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

Answer 1

a.
Number of socks that can be purchased = Amount available/Cost per socks
Number of socks that can be purchased = 104/2.60
Number of socks that can be purchased	40	socks
Zane can purchase 40 socks today.
b.
If zane invests his money is the risk free U.S Treasury security, then zane would receive the interest and principal payment at year end
Amount received	(104)*(1.11^1)
Amount received	115.44
Zane would have $115.44 at end of 1 year if he foregoes purchasing the socks today.
c
The price of socks would increase by 4% which is the inflation rate
Price of socks at end of year 1	2.60*1.04
Price of socks at end of year 1	2.704
d
At end of year 1, zane would have $115.44 in hand due to investment is U.S. security and price of stock would be $2.704
Number of socks zane can purchase at year 1	115.44/2.704
Number of socks zane can purchase at year 1	42.69
Change in purchase of socks	(42.69-40)/40
Change in purchase of socks	6.73%
In percentage terms zane can buy 6.73% higher socks.
e.
Real rate of return = (1+nominal rate of return)/(1+inflation rate) - 1
Real rate of return = (1.11)/(1.04) - 1
Real rate of return	6.73%
The change in purchase of socks by zane is equal to real rate of return.
The change in purchase of socks is equal to real rate of return as at the end of year 1 zane would use the amount received on investment which is based on nominal rate of return.
The purchase price considered would after inflation rate and therefore both are equal.