Question

1. XYZ Corp has a liability of 208,000 in two years, and it has assets of 100,000 now and 96,000 in one year. At a positive annual interest rate K%, XYZ's assets and liability are matched. Calculate K.

K is the number of percent, not the decimal value of the percent. For example in 12.5%, K = 12.5, not 0.125.

2. Determine whether the matching in Question 2 is Redington immunized, fully immunized, or not immunized. Which of the follow is correct?

A. None of these.

B. The matching is fully immunized.

C. The matching is not immunized.

D. The matching is Redington immunized, but not fully immunized.

Answer 1

Liability in 2 years = L = 208,000

Asset value now = A1 = 100,000

Asset value in one year = A2 = 96,000

since assets & liabilities for XYZ are matched at K%,

[A1*(1+K%)² ] + [A2*(1+K%)] = L

[100,000*(1+K%)² ] + [96,000*(1+K%)] = 208,000

By trial & error, and substituing different values of K in Left hand side of the above equation and the risght hand side of the above equation, we will find that at K = 4%, both sides become equal , that is , at K=4% , assets and liabilities for XYZ match.

Answer, K = 4