Question

During a certain year, the nominal interest rate was 7 percent, the real interest rate was 4 percent, and the CPI was 198.3 at the end of the year. The CPI at the beginning of the year was a. 192.5 b. 220.1 c. 204.2 d. 178.6

Answer 1

a) 192.5

Explanation:

Since we are given:

Real interest rate= 4%

Nominal interest rate= 7%

CPI for year end = 198.30

nominal interest rate 7%

real interest rate 4%

end of the year CPI is 198.30

beginning of the year CPI = ??

To find beginning of the year CPI, let's first find the difference between nominal rate and real interest rate, which is:

Nominal rate - real interest rate, we have:

7 - 4 = 3%

Formula for end of year CPI =

beginning of year CPI*[1+ (nominal rate - real interest rate)]

To find beginning of year CPI, let's make it the subject of the formula:

Beginning of year CPI =end of year CPI / (1 + 3%)

=198.30 / (1 + 0.03)

= 198.30/1.03

=192.52

Therefore, beginning of year CPI is 192.5