2025 TJC P1 Q7

Mabel and Janice decided to start a \(5\)-year savings plan beginning in January \(2026\).

Mabel saves using a piggy bank. At the start of January \(2026\), she deposits \(\$101\). Each subsequent month, she increases her deposit by \(\$1\)—so she deposits $\(101\) in January, \(\$102\) in February, \(\$103\) in March, and so on, until \(\$112\) in December. At the start of each new year, she resets her monthly deposit to \(\$101\) in January and repeats the same pattern through December. She continues this routine from \(2026\) to \(2030\), inclusive.

Janice, on the other hand, deposits $\(100\) at the start of every month into a bank account that earns \(0.3\)% interest per month, with interest calculated and added into the account at the end of each month.

1. Show that Janice will have more money in her savings account than Mabel has in her piggy bank at the end of December \(2030\).[5]
2. Find the month and year when Janice’s savings first exceed Mabel’s savings.[4]