Do I have to pay taxes on profit or interest earned by my offshore company?

No.

Most of the jurisdictions we work with do not impose taxes on profits made or interest earned by offshore company. Some, like Hong Kong or Delaware, only tax profits made within the jurisdiction, whereas Cyprus charges a 10% flat tax.

See more:

• Is it necessary for an offshore company in HK to submit audited accounts when it files its profits tax return?
• What is Delaware LLC tax rate?
• Disproving an old misconception: Cyprus Tax Haven

While a company may not be subject to tax reporting to its local authorities, from a personal standpoint it mustn’t relieve you from seeking counsel from a tax advisor in your country of residence in order to assess the extent of your own obligations, if any.