Management estimates that a new production process will save $$5,000$ in the first year, $$10,000$ the second year, and $$3,000$ the third year. Management expects a $30$ percent return on invested capital.

a$)$ How much capital could be invested in the new method to realize the savings described above?

b$)$ What is the present worth of the investment $($you calculated in a above$)$ AND the annual savings?

c$)$ What is the annual worth of the investment $($you calculated in a above$)$ AND the annual savings?

d$)$ What is the future worth of the investment $($you calculated in a above$)$ AND the annual savings?

e$)$ What is the present worth of investment and savings, if management invested $$10,000$ and still realized the same savings at i$=30\%?$

e$)$ What is the present worth of investment and savings, if management invested $$14,000$ and still realized the same savings at i$=30\%?$