I am trying to build a power bank to charge a 3.7V Lithium Ion battery and 200mAh. I was wondering if I could use a 3.7 V 700 mAh LiPo battery boosted to 5V with a dc dc boost module converter to charge it safely. I figured if I used the 3.7V LiPo battery without the converter then it would take forever to charge. I keep reading that a 4.2V charge is about the maximum voltage when charging a 3.7 V battery. I don't want to ruin the battery in the process of charging it with the power bank I am creating

 

Check out Battery University regarding charging and discharging lithium batteries safely. They are prone to catch fire or explode if treated incorrectly.
You might find these links useful :
http://batteryuniversity.com/learn/article/safety_concerns_with_li_ion
http://batteryuniversity.com/learn/article/charging_lithium_ion_batteries