2025 NYJC Promo Q8

Mr Tan decides to start a regular savings plan to save up for an overseas trip. At the start of the first month, he deposits $1000 and continues to deposit $800 at the start of every subsequent month. He withdraws \(10\%\) of the amount in the account at the end of each month for investment starting from the first month. The account pays no interest.

1. Show that the amount of money in the savings account at the end of the \(n\)th month is \(\$(7200 - 7000(0.9)^n)\).[3]
2. Find the earliest possible month such that the amount of money in the savings account first reaches $5000. Explain whether this occurs at the start or end of the month.[3]
3. State the amount of money that Mr Tan has in the savings account in the long run after withdrawing for his monthly investment.[1]
4. Find the total amount of money Mr Tan withdraws for investment at the end of 1 year.[2]