The only reference to banking money occurs in a parable which in its teaching has little to do with banks or money.
Luke 19:23 Wherefore then gavest not thou my money into the bank, that at my coming I might have required mine own with usury?
The word translated ‘bank’ is the Greek ‘trapeza’ and in context means the table or stand of a money changer, where he sits, exchanging different kinds of money for a fee, and paying back with interest loans or deposits.
The parable is about using one’s talents in the service of Christ; at the very least within the ecclesia (church) into which one is baptised.
Other than this parable the Bible says nothing about banking money.
Money has to be recognised as God given and used wisely in his service. We are not to become reliant upon it.
Matthew 6:19 Lay not up for yourselves treasures upon earth, where moth and rust doth corrupt, and where thieves break through and steal:
Matthew 6:24 No man can serve two masters: for either he will hate the one, and love the other; or else he will hold to the one, and despise the other. Ye cannot serve God and mammon.
We are not to hoard treasure upon earth but rather make provision to help others.
Luke 12:33 Sell that ye have, and give alms; provide yourselves bags which wax not old, a treasure in the heavens that faileth not, where no thief approacheth, neither moth corrupteth.
That is not to say that we are to sell everything that we own and make ourselves dependent upon others; rather that we strike a proper balance with what is surplus to our requirements in order to help others.
Israel, forbidden by the Law to lend upon usury to Israelites, was permitted to lend upon usury to gentiles.
Deuteronomy 23:19 Thou shalt not lend upon usury to thy brother; usury of money, usury of victuals, usury of any thing that is lent upon usury: 20 Unto a stranger thou mayest lend upon usury; but unto thy brother thou shalt not lend upon usury: that the LORD thy God may bless thee in all that thou settest thine hand to in the land whither thou goest to possess it.
Those who have believed the gospel and been baptised into Christ are not under the Law of Moses, but the principle of giving freely and not lending upon usury to the poor and needy stands.
Matthew 5:42 Give to him that asketh thee, and from him that would borrow of thee turn not thou away.
Ephesians 4:28 Let him that stole steal no more: but rather let him labour, working with his hands the thing which is good, that he may have to give to him that needeth.
There is no restriction upon saving money in a bank and receiving interest.
Our use of money, as with everything we do, should be done to the glory of God.
Colossians 3:17... whatsoever ye do in word or deed, do all in the name of the Lord Jesus, giving thanks to God and the Father by him.
I hope you have found this helpful.
May God bless you,