4. Peter sets up a savings plan. He makes an initial deposit of \(\pounds D\) and then pays in \(\pounds M\) at the end of each month. The value of the savings plan, in pounds, is modelled by $$u _ { n + 1 } = 1.025 u _ { n } + 1800$$ where \(n \geqslant 0\) is an integer and \(u _ { n }\) is the total value of the savings plan, in pounds, after \(n\) years.

1. Calculate the value of \(M\) Given that the value of the savings plan after 1 year is \(\pounds 6925\)
2. solve the recurrence relation for \(u _ { n }\)
3. Determine the value of \(D\)
4. Hence determine, using algebra, the number of years it will take for the value of the savings plan to exceed \(\pounds 20000\)