Policies offered by an insurer in an exemplary line of business have a coverage period of one year. Below there

are aggregate amounts of premium written in this line of business during first half of $2022,$ second half of

$2022,$ first half of $2023,$ and during the third quarter of $2023.$ Calculate the premium reserve as of $31$

September $2023.$

Assume that:

premium written is evenly distributed over the period of each half year, and also evenly distributed over the

period of July, August and September $2023,$

claims are evenly distributed over the $12-$month period of policy's validity