Payments of $1,000$ pa are payable quarterly in arrears from $1/1/20$ to $31/12/25.$

The annual effective rate of interest is $3\mathrm{.}4\%$ for calendar years $2020-2023($inclusive$)$ and $4\mathrm{.}2\%$

thereafter. Calculate:

$($i$)$ the present value of the payments at $1/1/20$

$($ii$)$ the accumulated value of the payments at $1/1/27$