$2.$ A firm would like to finance an investment by taking out a loan that requires $10$ fixed annual payments, with the first payment due in one year. The bank will require a return of $6\mathrm{.}5\%$ on this loan. The firm plans to borrow $$450,000$ using this loan.

a$.$ What will the firm$$s annual payments be$?$

b$.$ What would the first annual payment be$,$ if the firm wanted the annual payments to grow at a rate of $4\%$ each year?

c$.$ What would the last payment be$?$