Searching for 3240B.S.I balance spring

Thanks for posting. Double-check the length of the metal channel. Do not include the nylon fittings on either end in the measurement. If the channel is 33" long, then you likely have either an S380-33 or S385-33 Channel Balance. The only difference between these two balances is the depth of the bottom nylon shoe, or the 'heel-to-toe' measurement, so compare both with your old hardware to see what matches best. See the diagram below for reference. In either case, for a new stamp option choose 3240.

Comparison of the S378, S380 and S385 balance shoes.

It sounds like you have a Series 385 then. If the metal channel is 32" long however, then the stamp of 3240 is unusual--for a stamp beginning with '32-', normally the metal channel would be 33". Perhaps the balance was cut down to size by whoever installed the windows to ensured it fit. In any event, this means you'll need to take an extra step to choose the correct stamp option, which designates the strength of the balance. Weigh the window sash the balance supports. You can then match that exact weight with one of the weight ranges listed alongside each stamp option under the product description of the S385-32 product page.