Hello can you please answer this question below Thanks Suppo

Hello can you please answer this question below

Thanks

Suppose we observe the following rates: 1R1-6.3%, 1R2-71%, and E(251)-6.3%. If the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2? (Round your intermediate calculations to 5 decimal places and final answer to 2 decimal places. (e.g., 32.16)) Liquidity premium

Solution

1) (1 + 1R2) = [(1+1R1)(1+ E(2r1)+ L2)]^1/2 , where L2 = liquidity premium

  (1 + 0.071) = [(1+0.063)(1+0.063+ L2)]^1/2

1.071 = [(1.063)(1+0.063+ L2)]^1/2  

1.071 = [(1.063)(1.063+ L2)]^1/2  

(1.071)² = (1.063)(1.063+ L2)

1.147041 = (1.063)(1.063+ L2)

1.147041/ 1.063 = (1.063+ L2)

1.07906 - 1.063 = L2

1.61% = L2

2) a. future value of ordinary annuity = payment [(1+interest)^{number of payment} - 1 ] / interest

  = 4000 [(1+0.08)⁵ - 1 ] / 0.08

= 4000 [(1.08)⁵ - 1 ] / 0.08

= 4000 [(1.469328 - 1 )/ 0.08]

= 23466.4

b. future value of ordinary annuity = payment [(1+interest)^{number of payment} - 1 ] / interest

  = 4000 [(1+0.02)²⁰ - 1 ] / 0.02

= 4000 [(1.02)²⁰ - 1 ] / 0.02

= 4000 [1.485947 - 1 ] / 0.02

= 97189.4

c. future value of annuity due = (1+ interest) * payment [(1+interest)^{number of payment} - 1 ] / interest

= (1+ 0.08) * 4000 [(1+0.08)⁵ - 1 ] / 0.08

= (1.08) * 4000 [(1.08)⁵ - 1 ] / 0.08

= (1.08) * 4000 [1.469328 - 1 ] / 0.08

= 25343.71

d. future value of annuity due = (1+ interest) * payment [(1+interest)^{number of payment} - 1 ] / interest

= (1+ 0.02) * 4000 [(1+0.02)²⁰- 1 ] / 0.02

= (1.02) * 4000 [(1.02)²⁰- 1 ] / 0.02

= (1.02) * 4000 [1.485947 - 1 ] / 0.02

= 99133.19