2023 ASRJC Promo Q10

Customers who open a savings account with SRF bank will earn an interest rate of \(0.2\%\) per month based on the amount in the account on the last day of each month. The interest is added to the account at the end of each month.

1. Peter has a savings account with the SRF bank. He puts \(\$2000\) into his savings account at the beginning of each month starting from \({{1}^{\mathrm{st}}}\) January 2023. Find the amount he has in his savings account on \({{31}^{\mathrm{st}}}\) December 2027 after the interest has been added if no withdrawal is made. Show your workings clearly.[4]

2. Sandy, another customer of SRF bank, has retired from work starting \({{1}^{\mathrm{st}}}\) January \(2023\). Since then, she will no longer do any deposit of money into her own savings account with the bank. Instead, she will be using the money saved in that account for her monthly spending. She has \(\$750\,000\) in her SRF bank savings account on \({{1}^{\mathrm{st}}}\) January \(2023\).

   1. As she still has some money with her for her daily spending in January \(2023\), she will only commence her monthly withdrawal of \(\$k\) from her savings account in the middle of each month, starting from February \(2023\) onwards. Show that the amount of money in her savings account, at the end of \(n\) complete months from \({{1}^{\mathrm{st}}}\) January \(2023\), after the interest has been added, is given by \({{1.002}^{n}}\left( \$750\,\,000\right)-\$501k\left({{1.002}^{n-1}}\right)+\$501k\).

      [4]

   2. Taking \(k\) to be \(3000\), find the amount of money left in her savings account immediately after her last complete withdrawal of \(\$ 3000\).

      [4]