$2\mathrm{.}2$ You currently have R$10,000$ in a savings account that pays $1\%$ interest each

month and has monthly bank charges of R$10.$ You add R$400$ each month starting

at the end of the seventh month.

$2\mathrm{.}2\mathrm{.}1$ Derive a model for the amount in the bank account at any point in time.

$2\mathrm{.}2\mathrm{.}2$ Determine the amount in the account at the end of two years and a half.

$2\mathrm{.}2\mathrm{.}3$ Determine how long it would take for the amount in the account to reach

R$165,000.$