Company FM2 must pay 200,000 in 4 years. In order to fully immunized from changes in interest rate, the company invests in a 3 year zero coupon bond that matures for 90,000 and a 5 year zero coupon bond that matures for X. The actuary for Company FM2 determined that their portfolio fully immunized their ability to meet their obligations at the current interest rate i. Calculate X.

11.10%

Explanation:

The computation of the X is shown below;

The first equation is

$90,000 ÷ ( 1 + interest rate)^3 + X ÷ (1 + interest rate)^5 = $200,000 ÷ (1 + interest rate)^4

$90,000 × (1 + interest rate)^2 + X = $200,000 × (1 + interest rate)(I)

As we are assuming company has invested in both the bonds

So,

The second equation is

$90,000 (1 + interest rate)^2 = X (2)

By considering the both equation

we can derive that

X = $100,000 × (1 + interest rate)

Now the (1 + interest rate) is

= $100,000 ÷ $90,000

= 11.10%

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