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An insurance company is obligated to pay a policyholder $500 in one year and $2,000 in 3 years. The insurance company has decided to employ the dedication strategy. The following assets are available: 1 year zero coupon bond with annual effective yield of 7%. 3 year zero coupon bond with annual effective yield of 8%. Determine the cost of establishing the asset portfolio.

Sagot :

danialamin

Answer:

The total cost of establishing the portfolio is $2054.95.

Explanation:

The present value of a bond is given as

[tex]PV=FV\times\dfrac{1}{(1+r)^n}[/tex]

For 1 year zero-coupon bond is

  • FV is 500
  • r is 7% or 0.07
  • n is 1

So the value is

[tex]PV=FV\times\dfrac{1}{(1+r)^n}\\PV=500\times\dfrac{1}{(1+0.07)^1}\\PV=500\times\dfrac{1}{(1.07)}\\PV=500\times0.9346\\PV=\$ 467.29[/tex]

Similarly, for 3 years zero-coupon bond is

  • FV is 2000
  • r is 8% or 0.07
  • n is 3

So the value is

[tex]PV=FV\times\dfrac{1}{(1+r)^n}\\PV=2000\times\dfrac{1}{(1+0.08)^3}\\PV=2000\times\dfrac{1}{(1.08)^3}\\PV=2000\times0.7938\\PV=\$ 1587.66[/tex]

So the total cost is

Total Cost=Cost of  1-year zero-coupon bond+Cost of 3-years zero-coupon bond

Total Cost=$ 467.29+$ 1587.66

Total Cost= $ 2054.95

So the total cost of establishing the portfolio is $2054.95.

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