A consulting engineer bought a fax machine with one year$$s free maintenance. In the second year the maintenance cost is estimated at $$20.$ In subsequent years the maintenance cost will increase $$20$ per year $($that is$,$ third year maintenance will be $$40,$ fourth year maintenance will be $$60,$ and so forth$).$ The amount that must be set aside now at $6\%$ interest to pay the maintenance costs on the fax machine for the first six years of ownership is nearest to