r 1 = 4.5% r 2 = 4.9% r 3 = 5.6% r 4 = 6.4% Assuming a constant real interest ra

Question

           r1 = 4.5%    r2 = 4.9%     r3 = 5.6%     r4 = 6.4%

Assuming a constant real interest rate of 2 percent, what are the approximate expected inflation rates for the next four years? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

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

           r1 = 4.5%    r2 = 4.9%     r3 = 5.6%     r4 = 6.4%

Assuming a constant real interest rate of 2 percent, what are the approximate expected inflation rates for the next four years? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Explanation / Answer

Solution:

Fisher Formula Says that

(1+R) = (1+r) / (1+i)

where R = real Rate of interest , i = Inflation, =r nominal Interest rate

therefore i = (1+r) / (1+R) -1

1. putting Values in formula

inflation for one year maturity = (1+4.5%) / (1+2%) -1

= 2.45%

2. for Second year Formula is

i = ((1+r2) / (1+R) )^1/2 -1

i = 1.41%

3. For third years

use same formula with ^1/2 as ^1/3

i = 1.16%

4. for fourth year

use same formula with ^1/3 as ^1/4

i = 1.06%

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