V$.$ a$.$ Your long$-$lost rich third cousin has unexpectedly passed away at the age of $103.$ In her will, she arranged for you to receive a payment of $$10,000$ at the end of each year for the next eleven years. But the settlement lawyer handling her estate has offered you an immediate one$-$time payment of $$100,000.$ Is that a fair offer if the current interest rate is $6\%?$ Perform a financial calculation to answer the question. Show your work.

b$.$ After reading the fine print in your cousin's will, you noticed it states that the payment in the first year will be $$10,000$ but will be increased by $$500$ every year $($that is$,10500$ for next year, $11000$ for the year after that, and so on$).$ According to present value based upon the same interest rate as part a$,$ explain whether you should accept the offer from the settlement attorney. Show your calculation of present value.