2023 TJC P1 Q5

James puts \(\$500\) into an empty safe on 1 January 2023. On the first day of each subsequent month he puts \(\$10\) more than in the previous month, so that he puts \(\$510\) on 1 February 2023, \(\$520\) on 1 March 2023, and so on. On what date will he first have over \(\$10,000\) in total in his safe?[3]

Nora puts \(\$x\) on 1 January 2023 into a bank account which pays a compound interest at a rate of \(0.5\%\)per month on the last day of each month. She puts a further \(\$x\) into the account on the first day of each subsequent month. Given that she does not withdraw any money from her account, find the least integer value of \(x\) for which her account will accumulate at least \(\$50,000\) on 31 December 2027.[5]