Question

As of 12/31/2013, an insurance company has a known obligation to pay $1,000,000 on 12/31/2017. To fund this liability, the company immediately purchases 4-year 5% annual coupon bonds totaling $822,703 of par value. The company anticipates reinvestment interest rates to remain constant at 5% through 12/31/2017. The maturity value of the bond equals the par value. Consider two reinvestment interest rate movement scenarios effective 1/1/2014. Scenario A has interest rates drop by 0.5%. Scenario B has interest rates increase by 0.5%. Determine which of the following best describes the insurance company's profit or (loss) as of 12/31/2017 after the liability is paid.
А. Scenario A - (18,910), Scenario B - 19,190
B. Scenario A - (14,760), Scenario B - 14,420
C. Scenario A -(1,310), Scenario B - 1,320

Answer 1

Answer:

see explanation

Step-by-step explanation:

The n th term of a geometric sequence is

= a

where a is the first term and r the common ratio

Both a and r have to be found

Given a₃ = - 2, then

ar² = - 2 → (1)

Given a₇ = - 32, then

a = - 32 → (2)

Divide (2) by (1)

= , that is

= 16 ( take the fourth root of both sides )

r = 2 ← common ratio

Substitute r = 2 into (1)

a × 2² = - 2, that is

4a = - 2 ( divide both sides by 4 )

a = -  ← first term

Hence

= -  ← explicit formula

and

= -  ×  = - 0.5 × 512 = - 256

Explanation: