You purchased a $10-$year $$100,000$ TIPS bond with dividend of $4\%$ per year payable semiannually $($i$.$e$.,$ $$2,000$ every six months$).$ Assume there is no inflation adjustment for the first five years, but in years $6$ through ten, the bond face value increases by $$10,000$ each yea year compounded semiannually.

a$.$ What is the total net amount of money that you will have received during the ten$-$year life of the bond without any consideration of dividend reinvestment?

b$.$ What will be the equivalent future value for all the income received with dividend reinvestment included?