You are given the following spot rates: Time Spot Rate 0.25 2.2% 0.50 2.8% 0.75 3.1%...

You are given the following spot rates:

Time	Spot Rate
0.25	2.2%
0.50	2.8%
0.75	3.1%
1.0	3.7%

Consider a one-year interest rate swap with a notional value of 3000. Determine the swap interest rate per quarter.

Solutions

Expert Solution

Answer-

We need to first calculate the discount factors

Z 90 = 1 / 1 + [ ( 0.022 x 90 / 360) ]
Z 90 = 1 / [1 + 0.0055]
Z 90 = 1 / 1.0055
Z 90 = 0.9945

Z 180 = 1 / 1 + [ ( 0.028 x 180 / 360 )]
Z 180 = 1 / [1 + 0.014 ]
Z 180 = 1 / 1.014
Z 180 = 0.9862

Z 270 = 1 / 1 + [ ( 0.031 x 270 / 360 )]
Z 270 = 1 / [1 + 0.02325 ]
Z 270 = 1 / 1.02325
Z 270 = 0.9773

Z 360 = 1 / 1 + [ ( 0.037 x 360 / 360 )]
Z 360 = 1 / [1 + 0.037 ]
Z 360 = 1 / 1.037
Z 360 = 0.9643

The swap interest rate per quarter = 1 - Z 360 / ( Z 90 + Z 180 + Z 270 + Z 360)

The swap interest rate per quarter = 1 - 0.9643 / ( 0.9945 + 0.9862 + 0.9773 + 0.9643)

The swap interest rate per quarter = 1 - 0.9643 / 3.9223

The swap interest rate per quarter = 0.0357 / 3.9223

The swap interest rate per quarter = 0.009102

The swap interest rate per quarter = 0.9102 %

The swap interets rate annually = 0.9102 % x 360 / 90 = 3.641 %

For the notional value of 3000, the quarterly amount will be = 0.9102 % x 3000 = 0.009102 x 3000 = 27.306

jeff jeffy answered 1 year ago

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