Question $31(7$ points$)$

A financial engineer designs a new financial instrument that he calls, the Simplex.

This instrument gives the holder access to the following cashflows:

For the first $6$ years, the holder receives $$100$ per year starting next year $($a

total of $6$ payments$)$

The holder does not receive any cashflows for years $7,8$ and $9.$

Starting at the end of year $10,$ the holder receives $$75$ growing at a rate of $8\%$

per year forever

The holder has to pay a "service fee" of $$10$ every year starting at the end of

year $5$ ; this goes on forever.

The prevailing discount rate throughout is $10\%$

The financial engineer would like to determine a fair market price for this financial

instrument, what do you suggest this price to be$?$