2025 CJC P1 Q10

Mr Huat is saving for a car that he plans to buy in the future. He needs to save a minimum of \(\(150,000\). A savings plan allows him to deposit \)\(6,000\) into a savings account on the first day of every month. At the end of each month, the total amount in the savings account (including interest) is increased by \(3\%\). Mr Huat makes an initial deposit on \(1\) January \(2026\).

1. Show that the total amount, correct to \(2\) decimal places, in the savings account at the end of December \(2026\) is \(\(87,706.74\).[2]
2. Find the month and year in which the total amount in the savings account will first exceed \(\)150,000\). Explain whether this occurs on the first or last day of the month.[6]

Mr Huat can also choose to save regularly in a different savings account which offers no interest. He makes an initial deposit on \(1\) January \(2026\) of \(\(6,000\). On the first day of each subsequent month, he deposits \(\)d\) more than he deposited in the previous month.

3. Find, in terms of \(d\), the total amount in the savings account at the end of December \(2026\).[2]
4. Hence, find the minimum value of \(d\) such that Mr Huat can buy the car by end of December \(2026\). Give your answer correct to the nearest integer.[2]