Upon graduation you find yourself owing $$35,000$ worth of student debt to your bankers. Unfortunately, rates have risen from their recent lows and the terms of your repayment involved a $10-$year amortization period and a fixed interest rate of $7\%($monthly compounding$).$ Assume all payments are made at the end of each period.

a$)$ What is your monthly payment?

b$)$ How much will you still owe after $6$ years of payments?

c$)$ An external finance company offers you an alternative to this repayment scheme, suggesting you instead make $12$ annual payments of $$4,500$ to them. Which of the two offers to you prefer and why?