Question

Suppose the 1-year effective annual interest rate is 3.6% and the 2-year effective rate is 2.4%. Compute the fixed rate in a 2-year amortizing interest rate swap based on $330,000 of notional principal in the first year and $260,000 in the second year.

Please show calculations in detail. Thank you.

Answer 1

Answer :

EAR for first year = 3.6%,

so interest rate for year 1 = 3.6%

EAR for second year = 2.4% , so calculate the interest rate for 2nd year

[ ( 1 + 2.4% )^2 / ( 1 + 3.6% )^1 ] - 1

= [ ( 1.024 )^2 / ( 1.036 ) ] - 1

= 1.214%

Interest paid for first year = 330,000 ( 0.036 )

Interest paid for second year = 260,000 ( 0.01214 )

We need to set the present value interest streams of two years equal to each other , R being the swap interest rate

R : The present value of interest on variable rate = The present value of interest at fixed rate

[ 330,000 ( 0.036 ) / 1.036 ] + [ 260,000 ( 0.01214 ) ( 1.024 )^2 ] = [ 330,000 (R) / 1.036 ] + [ 260,000 (R) / (1.024)^2

11,467.18 + 3010.18 = 318,532.82 R + 247,955.32 R

14,477.36 = 566,488.14 R

R = 14,477.36 / 566,488.14

R = 0.02556 ( or ) 2.55%.