2015 NJC P2 Q2

Joanne begins a monthly savings plan. In the first month, she puts \(\$1000\) into her savings, and for each subsequent month she puts \(5\) more than in the previous month. How many months would it take for Joanne's total savings to first exceed \(\$20000\)?[3]

Jim starts a monthly savings plan two months later than Joanne with an initial savings of \(\$2000\), and for each subsequent month he puts \(\$100\) more than in the previous month. The table below shows the person whose total savings exceeds the other person's total savings in the \(N\) th month since Joanne started saving.

Find the value of \(n\).[3]

Suppose instead that Joanne puts a fixed amount of \(\$1000\) into her bank account on the first day of every month. The interest rate is \(r\%\) per month, so that on the last day of each month the amount in the account on that day is increased by \(r\%\). At the end of \(2\) years, the total amount in her account will be at least \(\$30000\). Find the smallest value of \(r\), correct to \(1\) decimal place.[3]