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.

159.2.

b.
168.3.

c.
185.5.

d.
196.1

Answer 1

CPI at the beginning of the year = 192.52

Step-by-step explanation:

given data

nominal interest rate = 7 percent

real interest rate = 4 percent

CPI = 198.3

to find out

CPI at the beginning of the year

solution

we know that according to fisher equation

1 + r =
`(1+n)/(1+i)` ....................1

and for smaller values is equivalent to r

r = n - i .....................2

here r is real interest rate and n is nominal interest rate and i is inflation rate

so from equation 2

4 = 7 - inflation rate

inflation rate = 3 percent

so

Rate of inflation = (CPI at the end of the year - CPI at the beginning of the year) × 100 ÷ CPI at the beginning of the year

put here value

3% = (198.3 - CPI at the beginning of the year) × 100 ÷ CPI at the beginning of the year

CPI at the beginning of the year =
`(19830)/(103)`

CPI at the beginning of the year = 192.52