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An insurance company must make payments to a customer of $8 million in one year and $4 million in four years. The yield curve is flat at 9%. a. If it wants to fully fund and immunize its obligation to this customer with a single issue of a zero-coupon bond, what maturity bond must it purchase?

Respuesta :

Answer:

  1.8356 years

Explanation:

The computation of the purchase of maturity bond is shown below:

Years (A)       Payment       PVF at 9%      PV                 Weight (B)   Duration (A × B)

1                  $8,000,000         0.9174   $7,339,449.54    0.7215    0.7215

4                 $4,000,000         0.7084  $2,833,700.84     0.2785    1.1142

                                                              $101,731,503.39   1             1.8356