Zack saves $\$x$ on 1 January 2024. On the first day of each subsequent month, he saves $\$10$ m

Question

Zack saves $\$x$ on 1 January 2024. On the first day of each subsequent month, he saves $\$10$ more than in the previous month, so that he saves $\$\left(x+10\right)$ on 1 February 2024, $\$\left(x+20\right)$ on 1 March 2024, and so on. Find the value of $x$ if he saves $\$25\,000$ in total on 1 December 2026.[3] Dan opens a savings account. He deposits $\$200$ on 1 January 2024 and continues to deposit $\$200$ on the first day of each subsequent month. The interest rate of the savings account is $0.2\%$ per month, so that on the last day of each month the amount in the account on that day is increased by $0.2\%$ Find how much the $\$200$ deposited on 1 January 2024 is worth at the end of 31 December 2024.[1] Show that, at the end of the $n$th month (where January 2024 is the first month, February 2024 is the second month, and so on), the total amount in the account is $\$100200\left({{1.002}^{n}}-1\right)$.[4] In which month and year will the amount in Dan’s account first exceed $\$4500$ Explain whether this occurs on the first or last day of the month.[4]

Accepted Answer

(a) $x=519.44$ (b)(i) $\$204.85$ (b)(ii) $\displaystyle \$100200\left((1.002)^n-1\right)$ (b)(iii) last day of October 2025

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