Funny you say that, I changed both recently.
I changed my battery 2 weeks ago.
Car failed to start 3-4 times, where I had to wait 20 seconds, and then it would start. I remembered it used to shutdown quickly last winter due to battery when I just wanted to listen a bit of radio. I still could charge the old battery full, but changing it wasn't a placebo, the new battery starts so quickly compared to the old one.
I changed the serpentine/tensioner/idler pulleys last week. Sound it was making was crazy annoying, so I changed all that and it's running like new now.
I took my time, did it at 0°C, and it took me about 1h30. Today, I could probably do it in less than 45 minutes. It costed me 260$CAD total.
I used this how-to from Kies Motorsports :
My 2015 35i has 86,000km.