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∣ = 586.411

Step-by-step explanation:

The effective interest rate is 0.05 so at the end of a year total amount will be 1.05 multiplied by principal

Liability = 6,000 ÷ 1.05^4 = Asset

Therefore

6,000 ÷ 1.05^4 = (A ÷ 1.05^2) + (B ÷ 1.05^6) (equation 1)

Multiply through by 1.05^6

6000(1.05^2) = A(1.05^4) + B

B = 6000(1.05^2) - A(1.05^4) (equation 2)

Finding differential from equation 1

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)

Multiply through by 1.05^6

4(6000 ÷ 1.05^2) = 2(A ÷ 1.05^4) + 6B

Substitute value of B from equation 2

4(6000 ÷ 1.05^2) = 2(A ÷ 1.05^4) + 6 *6000(1.05^2) - 6*A(1.05^4)

A= 2721.0884

Substitute A in equation 2

B = 6000(1.05^2) - 2721.0884(1.05^4)

B= 3307.5

∣A−B∣ = |2721.0884 - 3307.5|

∣A−B∣ = 586.411