Question

Aakash has a liability of 6000 due in four years. This liability will be met with payments of A in two years and B in six years. Aakash is employing a full immunization strategy using an annual effective interest rate of 5%.Calculate |A-B|

Answer 1

|A-B|= 586.411565

Explanation:

We know that = Liability

`PLiability= (6000)/(1.05^(4) )`

`(6000)/(1.05^(4) )=(A)/(1.05^(2) )+(B)/(1.05^(6) )\\\\6000(1.05^(2) ) = (1.05^(4) ) +B\\B= 6000(1.05^(2) )-(1.05^(4) )----------(1)\\\\`

dAssets =dLiability

`4=2*((A)/(1.05^2) )/((6000)/(1.05^4) ) +6*((B)/(1.05^6) )/((6000)/(1.05^4) ) \\4={(6000)/(1.05^4)= 2*(A)/(1.05^2) +6*(B)/(1.05^6)\\\\4[6000(1.05^2)]= 2*A(1.05^4)+6*B`

From equation 1 we have

`4[6000(1.05^2)]= 2*A(1.05^4)+6*6000(1.05^2)-6*A(1.05^4)\\4*A(1.05^4)=2*6000(1.05^2)\\A=(2*6000(1.05^2))/(4*(1.05^4)) \\A=272.088435\\`

Going back to equation 1 we have

`B= 6000(1.05^2)-A(1.05^4)\\B= 3307.5\\|A-B|= |2721.088435-3307.5|= 586.411565`