Each year Lin pays into a savings scheme. In year 1 she pays in \(\pounds 600\). Her payments then increase by \(\pounds 80\) a year, so that she pays \(\pounds 680\) into the savings scheme in year \(2 , \pounds 760\) in year 3 and so on. In year \(N\), Lin pays \(\pounds 1000\) into the savings scheme.
Find the value of \(N\).
Find the total amount that Lin pays into the savings scheme from year 1 to year 15 inclusive.
Saima starts paying into a different savings scheme at the same time as Lin starts paying into her savings scheme.
In year 1 she pays in \(\pounds A\). Her payments increase by \(\pounds A\) each year so that she pays \(\pounds 2 A\) in year \(2 , \pounds 3 A\) in year 3 and so on.
Given that Saima and Lin have each paid, in total, the same amount of money into their savings schemes after 15 years,