IV Compute the twoyear nominal interest rate using the exact

IV. Compute the two-year nominal interest rate using the exact formula and the approximation formula for each set of assumptions listed in (a) through (c). a. b. c. i.-2%; it+1-3% It = 2 %, i?1-1096 I.-290; it+1-3%. The term premium on a two-year bond is 1%

Solution

According to the exact formula,

2 year nominal rate of interest (that is, i₂) = [(1 + i_t) (1 + i^e_t+1)] - 1

However, according to the approximation formula,

2 year nominal rate of interest (that is, i₂) = i_t + i^e_t+1

a.

Exact formula =>  i₂ = [(1.02) * (1.03)] - 1 = 1.0506 - 1 = 0.0506

i₂= 5.06%

Approximation formula => i₂ = 2 + 3 = 5%

b.

Exact formula => i₂ = [(1.02) * (1.10)] - 1 = 1.122 - 1 = 0.122

i₂ = 12.2%

Approximation formula => i₂ = 2 + 10 = 12%

c. Let the term premium be defined as i_p.

Exact formula => 2 year nominal rate of interest (that is, i₂) = [(1 + i_t) (1 + i^e_t+1) (1 + i_p)] - 1

=> i₂ = [(1.02) * (1.03) * (1.01)] - 1 = 1.0611 - 1 = 0.0611

i₂ = 6.11%

Approximation formula => 2 year nominal rate of interest (that is, i₂) = i_t + i^e_t+1 + i_p

i₂ = 2 + 3 + 1 = 6%