A company estimates that it will need $$50,000$ in operating costs in the first year and this amount is projected to increase by $2\%$ each year for the next $10$ years. How much money should the company invest now, so that it will have enough funds to cover those costs for the $10$ years. Assume that the funds will be invested in an account that earns an interest rate of $8\%$ per year.

How much is the required initial investment?

A$.$ $$357,866$

B$.$ $$783,275$

C$.$ $$362,808$

D$.$ $$642,559$

How much will you have, if the interest rate was only $2\%$ per year $($instead of $8\%)?$

A$.$ $$597,546$

B$.$ $$357,866$

C$.$ $$543,871$

D$.$ $$490,196$