It sounds like the OP is just starting to dive. Has a few local dives he wants to do. Budget or supply issues are keeping him away from a dive computer. Wanting to dive, is a computer required? As stated many times, no. People dived for decades without a computer. It is more limiting, requires more operator skill in running a timer and depth gauge, but it can be done. Hopefully the OP was taught how to run a set of tables. For the 2 shallow dives a day the OP wants to do, just fine to use the tables and get real experience with them.
Long term, a computer is a very desirable piece of kit to own. You will want it. As you progress and get beyond the local spot you will find it very helpful.
So go enjoy your local dive spot. Run the tables, timer and depth gauge for now. But plan on eventually getting a computer. And as others stated, it might be more economical to just get a basic computer over a depth gauges and timer. But if the gear is just a rental for now, and it comes with a basic depth gauge, and you have a decent waterproof watch with timer. That is all you need.