Are the funds acquired monthly from the bank, whose value varies based on market fluctuations, permissible (halal)?

If the bank in which you invest your money is Islamic, adheres to Sharia-compliant transactions, and does not guarantee the principal while the profit is determined as a percentage, then there is no harm in that. However, if the bank is interest-based (riba-based), then it is absolutely impermissible to invest in it.