$1.$ Durango Mountain Bike Tours$$ ending cash balance as of December $31,2022$ was $$10,000.$ Its expected cash collections and payments for the next six months are given in the following table.

Month Collections Payments

January $$18,563$ $$21,825$

February $3088135100$

March $5107548600$

April $8184468344$

May $10968890113$

June $141750107100$

c$.$ If the firm must pay $5\%$ annual interest on its short$-$term borrowing, what are the ending cash balances for each month?

d$.$ What are the ending cash balances if the firm uses any cash in excess of the minimum to pay off its short$-$term borrowing for each month?