There are trade offs with a premium tank so the decision to buy one is not as simple as saying 'does it make more money?'
Firstly a premium tank is costly to purchase, the high tier ones with the best earning potential are 7500 to 12000 gold (£30-40) each
and there's no point in buying a premium tank without spending another 1000 gold on a 100% crew, you will also need to spend another million silver (2500 gold) to get Ventilation and a Rammer.
So that's a layout of approximately £50-60.
Secondly you need to know that the premium tanks are not the best tanks (apart from the Type 59 of course).
An equivalent tank of the same tier will generally out perform a premium tank by a small but appreciable margin.
Thirdly, for grinding out silver a premium account effectively doubles your income.
Although it only boosts your basic income by 50%, that is before you pay for repairs and ammo which can easily halve your final income, but with premium that 50% bonus to the gross amount works out as about 100% on the net profit.
Premium tanks only have a significantly reduced repair cost which is why they're good for grinding silver.
Fourthly you need to be at least an average to good player to really benefit from a premium tank, just turning up and going AFK in a premium tank is only minimally more effective than doing the same in any other tank.
You quality of play massively influences your income.
So yes, premium tanks can earn more money, but it's no as simple as buy premium > profit!
gaming.stackexchange.com/users/38245/A Pale Shadow
Yes, they are.
Especially because of their low repair costs premium tanks tend to net you more credits than a regular tank.
Having a premium tank is especially useful when you do not intent to play with a premium account, as the premium tank will then help you pay for the high tier non premium vehicles.
I own a type 59 myself, without a premium account it will make 30-60k for a win, and 5-20k for a lost battle.
gaming.stackexchange.com/users/11240/Xenox
Premium tank can help you to earn credits to cover expenses for high tier non-premium tanks.
Repair cost is low and profitability is much higher, you will earn more credits.
If you don't want to buy a premium account and still want to invest some money for high tier tanks, premium tank is your best choice.
You don't need to train your crew to 100% using gold, you can train your crew in battles as you do with the regular tanks.
You also don't have to spend gold for modules as mentioned, you can buy it with credits as well.
It is a one time investment, which will basically give you access to tier 9 and 10 tanks, because they are too expensive to play.
gaming.stackexchange.com/users/43515/Radium
If you are only buying Premium just for grinding or farming a credits, you better check this post about her guide for easy credits farming using premium tanks.
gaming.stackexchange.com/users/50466/Kyle
No one has mentioned training yet.
Any crew can use 100% of their skill in a premium tank of the same type and country (e.g. any medium crew from a US tank can run in a US medium premium with no penalty).
If you want your crew to gain experience faster, it's a reason to have a premium.
gaming.stackexchange.com/users/53744/Jeremy Miles
I see this advice given a few times on the World of Tanks forum: buy a premium tank to make silver/credits.  Are premium tanks really that much more effective at farming money than other tanks of the same tier?
Is it worth buying a premium tank?
gaming.stackexchange.com
<world-of-tanks>
gaming.stackexchange.com/questions/95415
gaming.stackexchange.com/users/38034/mechatankzilla
Premium tanks can earn more money. They help you earn credits to cover expenses. While it is not a simple question, it seems that buying premium tanks can benefit a player, in many ways.
Players suggesting the benefits of buying premium tanks.