Question

An insurance company has commited to make a payment of $100,000 in 10 years. In order to fund this liability, the company has invested $27, 919.74 in a 5 year zero-coupon bond and $27,919.74 in a 15-year zero-coupon bond. The annual effective yield on all assets and liabilities is 6%. Determine whether the company's position is immunized.

Answer 1

Hello,

Here is the solution -

PV of liability at 6% yield = 100000/1.06¹⁰ = $55839.48

PV of 5 year zero coupon bond = 27919.74/1.06⁵ = $20863.25

PV of 15 year zero coupon bond = 27919.74/1.06¹⁵ = $11650

Since sum of both zero coupon bonds PV < PV of liabililty , hence we can say that company's position is not immunized