Separate continuous payoff time from monthly rounding

In a loan scheme, the amount owed is $M$ dollars at time $t$ months; both variables are continuous. Interest increases the amount at a rate proportional to the amount owed, while repayment occurs at a constant rate of $500 per month. Interest and repayment balance when $M=10000$. An initial loan of $8000 is taken on 1 March 2013.

(i) Show $dM/dt=(M-10000)/20$.2 marks

(ii) Find $M$ in terms of $t$.4 marks

(iii) Find the date when the loan is cleared.2 marks