The relationship between husband and wife should be based on love, affection, cooperation, and mutual respect. According to Islamic teachings, the husband and wife are completely independent financially from each other, and it is the role of the husband to spend on the family according to his financial capacity.
Even if he is not obliged to inform the wife about where he spends the rest of his earning, it is preferable to do so out of compassion and mutual cooperation and respect.

Dr. Monzer Kahf, a prominent economist and counselor, stated: The fact is that marriage life is a life of love, cooperation, and mutual respect and accommodation. If one wants to insist on applying the legality of definition and boundaries, any mutual accommodative cooperation becomes out of question. This means that we only resort to legality when we fail in accommodating each other.

The legality of it is that husband and wife are completely independent financially from each other, none is required to inform or consult the other about what to do or how to do it and none of them has an obligation/right to tell or be informed. That is, of course, keeping in mind that the husband is required to spend on the family (wife and children) fairly and reasonably according to the extent of his resources and ability while the wife is not required to spend on her own needs or the needs of her children and household.

Moreover, the eminent Muslim scholar and renowned da`iyahSheikh `Abdel Khaliq Hasan Ash-Shareef added,

The husband is obligated only to spend on his wife and her needs and the needs of the house according to the financial capacity of the husband and the standard of living of the persons concerned. Almighty Allah says, [Let him who has abundance spend of his abundance, and he whose provision is measured, let him spend of that which Allah has given him. Allah asks naught of any soul save that which He has given it] (At-Talaq 65:7).

So, if the husband spends on his wife and the family fairly, then he fulfills the obligation, and after that he is not obliged to tell his wife about what he does with his earnings. If he saves some of his earnings or spends on his parents or any of his relatives or gives some of his earnings in charity for the sake of Allah, then he is not obliged to his tell his wife about that.
Yet, if he told her out of compassion, love, and cooperation on doing good and in order not to cause her to feel any doubt regarding it, this will be preferable.