Question

The table below shows the prices (P) and quantities (Q) of a typical consumption basket, which consists
of only product X and Y, for a country in several years:

a. Using year 2000 as the base year, calculate the CPI in 2000, 2007 and 2008.
b. What was the annual inflation rate between year 2007 and 2008?
c. A person took out a one-year loan of $550 from the bank in 2007 and repaid $594 in 2008. What was
the annual nominal interest rate between 2007 and 2008? What was the annual real interest rate?
d. Was the one-year loan a good business for the bank or not? Explain.

	2000	2007	2008
Product	Q P	P	P
X	5 $2	$3	$3
Y	10 $4	$4	$4.55

Answer 1

a)

Value of basket in 2000=Co=5*2+10*4=$50

Value of basket in 2007=C1=5*3+10*4=$55

Value of basket in 2008=C2=5*3+10*4.55=$60.50

CPI in 2000=(Co/Co)*100=(50/50)*100=100

CPI in 2007=(C1/Co)*100=(55/50)*100=110

CPI in 2008=(C2/Co)*100=(60.50/50)*100=121

b)

Annual inflation rate between 2007 and 2008=(CPI in 2008-CPI in 2007)/CPI in 2007)

=(121-110)/110=10%

c)

Nominal Rate of interest=(594-550)/550=8%

Real interest rate=Nominal interest rate-Inflation rate=8%-10%=-2%

d)

We can see that real interest rate is negative. It means that bank has a negative return in real terms.

It was not a good business for bank.