2020 CJC P1 Q10

Mr Lim is considering an education endowment plan for his child- EduPlan Awesome allows him to contribute \(\$300\) into the account on the first day of every month. At the end of each month, the total in the account is increased by \(0.3\%\).

1. Mr Lim contributes \(\$300\) on 1 January 2020 and continues to contribute \(\$300\) on the first day of each subsequent month.
   1. Show that the total amount in the account at the start of the \({{n}^{\mathrm{th}}}\) month (where January 2020 was the \({{1}^{\mathrm{st}}}\) month, February 2020 was the \({{2}^{\mathrm{nd}}}\) month, and so on) is \(\$A\left({{1.003}^{n}}-1\right)\),where \(A\) is an integer to be determined.[3]
   2. Hence, find the total amount in the account at the start of l January 2021, giving your answer correct to \(2\) decimal places.[1]

EduPlan Blessing allows him to contribute \(\$k\) into the account on the first day of every month. At the end of each month, the account earns a bonus and is added to the account. This bonus is \(\$0.01k\) for the first month, and for each subsequent month, the bonus is \(\$0.01k\) more than the bonus in the previous month.

2. State the amount of bonus earned for the \({{20}^{\mathrm{th}}}\) month, giving your answer in terms of \(k\).[1]
3. Find the total amount in the account at the start of the \({{n}^{\mathrm{th}}}\) month , giving your answer in the form \(0.005nk\left( n+B \right)\), where \(B\) is an integer to be determined.[3]

Mr Lim wishes to cash out the education endowment plan on 1 January 2040 when he makes his first monthly contribution on 1 January 2020.

4. Find the value of \(k\) such that both EduPlans have equal value when the education endowment plan is cashed out, giving your answer correct to the nearest whole number.[3]
5. Given that Mr Lim has other financial commitments, explain which EduPlan is the better option for him.[2]