Spicer & Co has budgeted its credit sales as follows:

June $ $600,000$

July $ $600,000$

August $ $800,000$

September $ $1,200,000$

October $ $1,400,000$

November $ $1,600,000$

Collections of credit sales are normally as follows:

Collected within $30$ days of the end of the month of sale: $50\%$

Collected in $30-60$ days: $30\%$

Collected in $60-90$ days: $15\%$

Uncollectible: $5\%$

The cash balance on $1$st October is expected to be $$200,000.$

Cash payments are expected to total $$800,000$ each month for July to November.

The cash balance at the end of October is expected to be $\_\_\_\_\_\_\_\_\_\_.$