Question

Peter saved $20000 in a time deposit account last year, and he can get back $22600 today. During this year, the consumer price index changes from 115 to 120.
With the above information,
a) Calculate the nominal interest rate.
b) Calculate the real interest rate.

Answer 1

a)

Nominal interest rate(i)=(FV/PV)^(1/n)-1

FV=future value =22600

n=years=1

PV=present value or principal amount =20000

i=(22600/20000)^(1/1)-1

=0.13

=13%

the nominal interest rate is 13%

=====

b)

Inflation rate =((CPI of the year -CPI of last year)/CPI of last year)*100

=((120-115)/115)*100

=4.34782609

=4.35%

By Fisher's exact formula:

r=(i-e)/(1+e)
r=i-e
r=real interest rate
e=inflation rate
i=nominal interest rate

r=(0.13-0.0434782609)/1.0434782609=0.0829166666=8.29%

By Fisher's approximation formula:

r=i-e

r=13-4.34782609=8.65217391=8.65%