a$)$ Steve is planning for his retirement life. She plans to invest an equal sum of $$30,000$ at the end of every year for the next $30$ years starting from the end of next year. Bank gives $20\%$ interest rate. Find the maturity amount of her account after $30$ years.

b$)$ A construction company is considering making a uniform annual investment in a fund with a view toward providing capital at the end of $7$ years to replace an excavator. An interest rate of $6\%$ is available; what is the annual investment required to produce $$50,000$ at the end of the period?