We report on an observationally constrained analytical model, the INterplanetary Flux ROpe Simulator (INFROS), for predicting the magnetic-field vectors of coronal mass ejections (CMEs) in the interplanetary medium. The main architecture of INFROS involves using the near-Sun flux rope properties obtained from the observational parameters that are evolved through the model in order to estimate the magnetic field vectors of interplanetary CMEs (ICMEs) at any heliocentric distance. We have formulated a new approach in INFROS to incorporate the expanding nature and the time-varying axial magnetic field-strength of the flux rope during its passage over the spacecraft. As a proof of concept, we present the case study of an Earth-impacting CME which occurred on 2013 April 11. Using the near-Sun properties of the CME flux rope, we have estimated the magnetic vectors of the ICME as intersected by the spacecraft at 1 AU. The predicted magnetic field profiles of the ICME show good agreement with those observed by the in-situ spacecraft. Importantly, the maximum strength (10.5 ± 2.5 nT) of the southward component of the magnetic field (Bz) obtained from the model prediction, is in agreement with the observed value (11 nT). Although our model does not include the prediction of the ICME plasma parameters, as a first order approximation it shows promising results in forecasting of Bz in near real time which is critical for predicting the severity of the associated geomagnetic storms. This could prove to be a simple space-weather forecasting tool compared to the time-consuming and computationally expensive MHD models.