Gabe would like to accumulate $$9,000$ at the end of $8$ years by making deposits at the beginning of each year for $8$ years. His first deposit will be $700$ and each subsequent deposit will increase by k$\%.$ You are also given that Gabe can invest at an annual effective interest rate of i $=4\%.($i$)$ By considering the present value at t $=0$ show that $9000$v$8=700$a$8,$i$$ and that $5876\mathrm{.}21=700$a$7,$i$$ where v $=(1+$i$)1$ and i$$ is a function of i and k$.($ii$)$ Given that i$=0\mathrm{.}04346,$ show that k $=8\mathrm{.}725.$