I was working on the following problem and the answer that was given to me looks a little shady and I wanted someone to confirm my thoughts.
As of 12/31/2005, an insurance company has a known obligation to pay $700,000$ on 12/31/2010. To fund this liability, the company immediately purchases 5-year $r=7\%$ annual coupon bonds totaling $F=499,091$ of par value. The company anticipates reinvestment interest rates to remain constant at $i=7\%$ through 12/31/2010. The maturity value of the bond equals the par value.
Contrary to the insurance anticipation interest rate decreased by 1/2% effective 1/1/2010 and stayed that way till 12/31/2010. Compute the insurance company's loss as of 12/31/2010 after the liability is paid
My claim is this. From bold part of the sentence, the last year of the reinvestment is what has reduced its value. Thus I am thinking
$$Frs_{\overline{4}\rceil 7\% }\times (1.065)+F(1+r)=AV_5$$
represents the accumulated value at time 5.
Since $700,000$ is what needs to be paid and $AV_5\approx 699,225.37$ is what I got, the amount that the company lost is the difference, $698.006$.
However, the answer in the problem tells me that the answer should be $1996$ claiming that
$$Frs_{\overline{5}\rceil 6.5\% }+F=AV_5$$
basically saying that the decrease in the reinvestment rate started since day 1.
Although I am pretty confident with my argument, I want to be cautious because I have a test coming in a month, so I would like some confirmation.
This doesn't sound right, does it?