The better quality ammo you load, the more you save.
Just another twist to highlight some potential for bigger savings.
For plinking you can save money as others have shown, but compare what you are making with the same quality ammo and the savings is big. One thing I look at is that when I reload I am getting real quality ammo, which is much more expensive to buy.
I do not always do the following, becuase if I'm gonna shoot paper I use lead swc bullets that I get real cheap from a local guy who casts, but many times I make real good ammo for long term storage, and that saves lots of money:
For instance, a box of WWB .38 spl is cheap, whereas a box of 125gr +p jhp personal defense loads is not. (The good personal defense loads are about $1 each or more, a box of 20 for $20-25). After I shoot up those initial cheap fmj rounds, I reload the cases with good jhp bullets right at +p pressure. Now I have some serious ammo to add to my rainy day collection. ( no I don't carry with handloads, only factory stuff But, if I ever need SD ammo, I would use handloads if I had to.)
I pay a bit more for my bullets, buying 125gr HPs usually, and can still reload for less than the price of WWB FMJ, or LRN. The cost is only slightly less than the cheap stuff, but a whole lot less considering that I am producing top quality loads.
If you ever get into it, hunting ammo is where the savings adds up big time, I still save money even over the cheapest hunting ammo I can buy. For instance,Rem. 30-30 150gr core-lockt is cheap at 14.97 per box of 20 rnds. $149.70 per 200 rounds. However, I get my brass for free at the range and from what I've saved over the years, so I can reload 200 rounds of the same ammo for around $60.
Premium .308 ammo is over $40 per box of 20, and I can make my own for under $7 per box, with premium bullets boosting the cost to somewhere around $9 per box.
If I could afford to buy powder and bullets in bulk, I could save even more. Plus it's fun. Good luck with whatever you choose.