1. An insurance company has a liability stream of $137 payable at time 8, $6 at time 9, and $5.55 at time 10. Assume a rate of interest of 5%.
   1. Calculate the present value (PV) of the above liability stream.
   2. Calculate the duration of the above liability stream.

Now assume the company purchases a bond to cover this liability stream which pays a coupon of $5 each year until redemption at time 10 and par value of $100.

3. Calculate the PV of the bond at 5%.
4. Calculate the duration of the bond