A student saves \(\$10\) on 1 January 2009. On the first day of each subsequent month she saves \(\$3\) more than in the previous month, so that she saves \(\$13\) on 1 February 2009, \(\$16\) on 1 March 2009, and so on. On what date will she first have saved over \(\$2000\) in total?[5]
A second student puts \(\$10\) on 1 January 2009 into a bank account which pays compound interest at a rate of 2% per month on the last day of each month. She puts a further \(\$10\) into the account on the first day of each subsequent month.
How much compound interest has her original \(\$10\) earned at the end of 2 years?[2]
How much in total is in the account at the end of 2 years?[3]
After how many complete months will the total in the account first exceed \(\$2000\)?[4]