All I'm saying is having a drug and/or alcohol problem might be cheaper than having a coin collection! 😉
I joke, of course. You're doing the right thing by staying away from them. 🙂
It is an unfortunate situation you're in, and I can very much sympathise. But to reiterate what the others have said, it's not really worth trying to hide it (too much). One of my old buddies tried hiding his completely, and it ended up causing a massive argument when they discovered his coin stash. (Fortunately, I was on hand to save his collection.)
I think your best cause of action is to be quite open and clearly dedicated to it. But basically try and keep yourself at the "swapping at face value" level for a few years. This way you're not losing money (as it's always worth face value), or at least not very much.
You can always collect rarer things later.
If you can, let your friends know you'll swap like-for-like (with maybe a small extra to make it worth their while. Depends on the quality of friends).
If you can, get yourself a part-time job or do odd jobs for neighbours, or extra chores about the house. Show your parents you're willing to put work into your collection. Let the people you're working for know you're a collector. They might just put things aside to pay you with.
Right now, your parents probably look at it as a silly hobby where you'll spend money and then get bored of it in a few months time. And they're trying to protect you from being wasteful, which is fair enough on their end.
You need to demonstrate that it's not “just a phase” but that'll come with time.
Until then, satisfy yourself with low value coins from circulation. Try and build a small network of people who can collect for you, and try to find a way to raise the additional funds to cover your hobby.
That's what I did at school age. Worked as a paper boy, used that money to trade coins off my friends (with a small premium based off the “rarity” of the coin).
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One other tip which might help convince your parents. Research anything that appears on a commemorative coin. Usually, nations put on things that they may be proud of.
A cursory glance at the India catalogue suggests you've got a good amount of 1/5/10 Rupee coins featuring statesmen, saints, and a few organisations too.
So if you get a coin with something like that on, learn why this person (or thing) was on a coin. You can then talk about that and it shows an interest in your country and it's heritage. Essentially, you're playing on the patriotism of your parents. They want you to be proud of India, you learnt unusual history of India through your coins.
Obviously, you'll know what's interesting to them better than I do.
For example, my mother loves architecture. About the same time, we released a bunch of coins with bridges on. So when we visited those bridges in passing on holiday, I could go “Did you know this bridge…”, and she'd ask why I knew that, “Why, this bridge was on our £1 coin last year”, and she'd go “huh, that's cool”.
We both appreciated the same thing, but through different routes. It might work, it might not.
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Anyway, I think I've typed enough. 😛
Whatever you do, don't let it interfere with your school work though. That should always come first. 🙂