Battery life calculation using Nano, NRF24L01+ and window magnetic reed switch
The components you've selected are impropriate (assuming you selected items from Amazon):
https://www.amazon.com/ATmega328P-Microcontroller-Board-Cable-Arduino/dp/B00NLAMS9C
and...
https://www.amazon.com/Makerfire-Arduino-NRF24L01-Wireless-Transceiver/dp/B00O9O868G?th=1

The Nano has extra components (LEDs, regulator and Serial/USB chip) on it that are not required. These will require power even when you put the MCU to sleep. 

The NRF24L01 is ok, but won't run on 3 x 1.5 V batteries. This unit has no onboard regulator (which is correct for your application) but would only be suitable for 2 x 1.5 V cells