Question

Consider the following spot interest rates for maturities of one, two, three, and four years.

r1 = 3.9% r2 = 4.5% r3 = 5.2% r4 = 6.0%

Assuming a constant real interest rate of 2 percent, what are the approximate expected inflation rates for the next four years?

I1		%
I2		%
I3		%
I4		%

Answer 1

[1+ Inflation rate] = [1+Nominal rate of return]/ [1+ Real rate of return]

Real rate of return = 2% = 0.02

Nominal rate = 3.9% = 0.039

[1+ Inflation rate] = [1+0.039]/[1+0.02]

[1+ Inflation rate] = [ 1.039]/[1.02]

[1+ Inflation rate] = 1.0186

Inflation rate = 1.0186-1 = 0.0186 = 1.86%

I1 = 1.86%

Similarly by replacing nominal rate to 4.5% we can find I2,5.2% we can find I3 and 6.0% we can find I4

Inflation rate for 2 years = [1+0.045]/1.02]-1

Inflation rate for 2 years = 2.45%

I2 = 2.45/2 years = 1.225% per year

Inflation rate for 3 years = [1+0.052]/1.02]-1

Inflation rate for 3 years = 3.14%

I3 = 3.14/3 = 1.045%

Inflation rate for 4 years = [1+0.06]/1.02]-1 = 3.92%

I4 = 3.92/4 = 0.98%