Independent solution

How to solve this Cash-Flow and Risk Matching question

Setup

Setup

Use the liability date as the comparison time; the earlier asset is accumulated two years and the later asset is discounted back from its unknown date.

300000(1.04)2+X(1.04)8−y=1000000300000(1.04)^2+X(1.04)^{8-y}=1000000

Model

Model

Full immunization with two assets straddling the liability date requires both value and first-order sensitivity to match.

600000(1.04)+(8−y)X(1.04)7−y=0600000(1.04)+(8-y)X(1.04)^{7-y}=0

Compute

Compute

Eliminating the discounted value of the second asset gives its payment year, after which its nominal amount follows from the value equation.

y=8.9607,X=701459y=8.9607,\qquad X=701459

Answer

Answer

The required later payment is approximately 701,500, so choice D is the listed result.

X≈701500(D)\boxed{X\approx701500\quad\text{(D)}}