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

a) 192.5

Step-by-step 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

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional