Robert secured a lease on a machine by paying $$1,950$ as a down payment and then $$550$ at the beginning of every month for $4$ years. The lease rate was $3\mathrm{.}50\%$ compounded monthly.

a$.$ What was the principal amount of the lease?

Round to the nearest cent

b$.$ What was the cost of the machine?

Round to the nearest cent

c$.$ What was the amount of interest paid over the term of the lease?