Question

Please answer

Compute the two-year nominal interest rate (12) using the exact formula and the approximation formula for each set of assumptions listed in the following tables. The assumptions are in each table's first three columns: they give values for the current one-year interest rate (u), next year's expected one-year interest rate ), and the term premium on a two-year bond (x). Enter your response for the approximate rate as calculated for the exact rate, round your response to three decimal places. Term Premium Exact tot 4% Approx. 12 3% 0%

Answer 1

It is given that the term premium is 0%

To calculate the exact value of i_2t we will have to calculate the cashflows from the bond and discount them with the current interest rate (i_1t) and the estimated interest rate in the 2^nd year (i^e_1t+1 )

Thus,
Bond face value = (i_2t X FV) / (1+i_1t ) + (i_2t X FV + FV) / (1+i^e_1t+1)²

For calculation purposes, let us assume the bond face value = 100
Thus, 100 = (i_2t X 100) /(1+ 3%) + (i_2t X 100 + 100) / (1+ 4%)²

100 = (i_2t X 100)/1.03 + (1+i_2t ) X 100/ 1.04^2
100 = i_2t X 97.087 + i_2t X 92.456 + 92.456
7.544 = 189.549 X i_2t
Solving for i_2t = 3.980%

We have calculated the exact rate above.

The Approx i_2t = (i_1t + 2 X i^e_1t+1 ) / 3

= (3% + 2 X 4%) /3 = 3.667%

i1t	i01t+1	Term Premium	Exact i2t	Approx i2t
3%	4%	0%	3.98%	3.67%