We use functionalized iron oxide magnetic multi-core particles of 100 nm in size (hydrodynamic particle diameter) and AC susceptometry (ACS) methods to measure the binding reactions between the magnetic nanoparticles (MNPs) and bio-analyte products produced from DNA segments using the rolling circle amplification (RCA) method. We use sensitive induction detection techniques in order to measure the ACS response. The DNA is amplified via RCA to generate RCA coils with a specific size that is dependent on the amplification time. After about 75 min of amplification we obtain an average RCA coil diameter of about 1 mu m. We determine a theoretical limit of detection (LOD) in the range of 11 attomole (corresponding to an analyte concentration of 55 fM for a sample volume of 200 mu L) from the ACS dynamic response after the MNPs have bound to the RCA coils and the measured ACS readout noise. We also discuss further possible improvements of the LOD.