Independent solution

How to solve this Immunization and Asset-Liability Management question

Setup

Setup

Discount the single liability and note that its Macaulay duration equals its two-year payment time.

L=600000(1.046)−2=548387.922304L=600000(1.046)^{-2}=548387.922304
DL=2D_L=2

Model

Model

Let the discounted asset maturity values match both liability present value and duration.

x1.046+y(1.046)4=L\frac{x}{1.046}+\frac{y}{(1.046)^4}=L
x1.046+4y(1.046)4=2L\frac{x}{1.046}+4\frac{y}{(1.046)^4}=2L

Compute

Compute

Solving gives one-year present-value weight 365591.95 and maturity amount x = 382409.18.

x1.046=365591.948203\frac{x}{1.046}=365591.948203
x=382409.177820x=382409.177820

Answer

Answer

The one-year zero matures for approximately 382,400, so choice D is correct.

x≈382400(D)\boxed{x\approx382400\quad\text{(D)}}