How to pronounce finance
Personally, I would ask you what part of speech does finance fall to. Finance can either be used as a verb or a noun. Finance in noun means the money used in investing or the money at hand to run the affair of your personal needs, government, or corporations.
Finance as a verb is the act of studying the investment or studying the money at hand for investment. Getting the right pronunciation of finance depends on the context in which it is used. If it would be used in the context as a verb or as a noun. The stress put on the verb finance is different from the stress that would be put on finance in noon because they will mean two different things.
According to the oxford dictionary,
Finance, (especially British English) (usually North American English financing) [uncountable]
Finance (for something) money used to run a business, an activity, or a project 1
Finance for education comes from taxpayers.
E.g. the project will only go ahead if they can raise the necessary finance.
Financing, [uncountable] the activity of managing money, especially by a government or commercial organization 2
The Minister of Finance
The finance director/department
A diploma in banking and finance
The world of high finance (= finance involving large companies or countries).
Finances [plural] the money available to a person, an organization, or a country; the way this money is managed 3
It’s about time you sorted out your finances.
Moving house put a severe strain on our finances.
The firm’s finances are basically sound.
Most people don’t understand the rudiments behind the origin of the word that is why the word is pronounced anyhow by different people.
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The finance with sound FIN-ANCE is the noun while the finance with the sound FINE-ANCE is the verb. They both sound differently. To use the verb or the noun, it depends on the context in which it is been used. If you are talking or referring to the money used to run the affair of something or the money at hand, you use the pronunciation with the sound FIN-ANCE while if what you are talking about is about how the affairs are being managed using investment, you use the pronunciation with the sound FINE-ANCE.
Using the English dictionary as an example, it talks about finance in different ways.
The management of money and other assets.
The science of management of money and other assets.
(Usually in plural) Monetary resources, especially those of a public entity or a company.
Who’s really in charge of a democracy’s finances?
Translations (management of money and other assets)
Translations (the science of management of money and other assets)
Translations (monetary resources)
(Finances, present participle financing; past and past participle financed)
To provide or obtain funding for a transaction or undertaking; to back; to support.
His parents financed his college education.
He financed his home purchase through a local credit union.
(Provide or obtain funding for) fund
Translations (to obtain or provide funding for a transaction or undertaking).
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If you actually look into the English dictionary meaning of finance under the part of speech verb, you would notice it emphasizes action which is ‘funding’. If we should look well into the finance proscriptions above, you will notice if it should be pronounced that way, the pronunciation will be FINE-ANCE which is the verb pronunciation of finance. It has become controversial between the Americans and the BRITS on the correct pronunciation of this word. Even in the French or Italian language, if the word finance and finanza respectively were to be translated to English, it would give the finance with the verb sound which is the FINE-ANCE.
So personally I would say the correct pronunciation of finance is the one with FINE-ANCE but if the context required the difference in which may be, for example, you say ‘I have my finances’ I would suggest you use the noun pronunciation as FIN-ANCE because, in that context, the word finance is serving as the name of thing which follows the NOUN definition which is the ‘naming word’.