Question

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

r_1 = 4.8%; r_2 = 5.2%; r_3 = 5.9%; r_4 = 6.5%

What is the percentage forward rate f_(1,3), where f_(1, k) refers to a forward rate for the period beginning in one year and extending for k years?

(Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Answer 1

To compute the forward rate we will use the following formula:

[ 1 + r ( T* + K ) ]^{( T* + K )} = [ 1 + r ( T* ) ]^T* x [ 1 + f ( T* , K ) ]^K

= In the above formula these are the notations used:

r = Rate of Interest

T* = Time after which the loan will start, which in our case is 1 year

K refers to the tenure of the loan which in our case is 3 years

Now we shall plug the above figures in the formula mentioned above:

[ 1 + r ( 1 + 3 ) ]^{(1 + 3)} = [ 1 + r (1) ]¹ x [ 1 + f (1 , 3 ) ]³

r (1 + 3 ) = Rate of interest of year 4 = 6.5 % or 0.065

r (1) = Rate of Interest of year 1 = 4.8% or 0.048

Plugging these figures in the above mentioned equation we will get

(1 + 0.065 )⁴ = (1 + 0.048)¹ x [(1 + f (1,3) ]³

= By solving the above equation we will get percentage forward rate of f_(1,3) to be equal to 7.07% approximately.

Feel free to ask in case of any queries regarding this question.