iPhone 5s Battery Replacement

Hello everyone, I have an iPhone 5s A1530 (32GB iOS 10.2) which is facing battery issues since last 2 weeks. It just switches off at 20% battery (in low power mode) and at 35-40% ( in Normal mode). It then just shows the low battery sign and restarts only after I connect it to the charger. I already tried to restore it with iTunes but the issue was still there. I've also tried to calibrate the battery but still no luck. My warranty expired 3 weeks back so now I have to pay for the battery replacement. I talked with the nearby apple service center and they are charging me 7000rs. (around 102 US$) just for the battery replacement. So I wanted to ask whether replacing the battery would fix the issue or can there be any other hardware issues which can cause this problem? Thank You.