You invest $$5,000$ at time t $=0,$ an additional $$3,000$ at t $=1/4,$ take out $$1,000$ at t $=1/2,$ and add $$4,000$ at t $=3/4.$ You have $$8,250$ at t $=1/4,$ $$8,000$ at t $=1/2,$ $$12,400$ at t $=3/4$ and $$12,975$ at t $=1.(1)$ Find the dollar$-$weighted rate of return on this investment. $(2)$ Find the time$-$weighted rate of return on this investment.