Sequence and Series - Geometric Progression

The Acme insurance company sells two savings plans, Plan A and Plan B.

For Plan A, an investor starts with an initial deposit of \( \$ 1000\) and increases this by \(\$ 80\) each month, so that in the second month, the deposit is \(\$ 1080\), then ext month it is \(\$1160\) and so on.

For Plan B, the investor again starts with \(\$ 1000\) and each month deposits \(6\%\) more than the previous month.

1. Write down the amount of money invested under Plan B in the second and third months.[2]

Give your answers to parts (b) and (c) correct to the nearest dollar.

2. Find the amount of the \(12^{\mathrm{th}}\) deposit for each Plan.[4]
3. Find the total amount of money invested during the first \(12\) months
   1. under Plan A;[2]
   2. under Plan B.[2]