To answer the question, we need to first clarify that when you say mutual funds, individuals mean equity mutual funds. Equity mutual funds are mutual funds which invest bulk of the money in equity shares.

Now, let us see whether bank deposits have given better returns or equity mutual funds. Let us take some of the top mutual funds in India and check their returns over 3 years and 5 years.
| Name of Fund | 3 year returns | 5 year returns |
| HDFC Equity | 26.14% | 14.40% |
| Birla Sun Life Frontline Equity Fund | 9.00% | 9.31% |
| Franklin India Prima Plus Fund | 28.06% | 16.69% |
| SBI Magnum Multiplier Fund | 28.49% | 14.42% |
| ICICI Prudential Focused Bluechip | 23.47% | 14.21% |
| L&T India Large Cap Fund | 22.92% | 12.57% |
Now, as can be seen from the table most of the equity mutual funds have generated super returns in the last 3-5 years. In fact, the 5 year returns of these schemes easily beat returns of bank deposits, which even with compounding interest every quarter would have given you a maximum returns of 13-14 per cent.
Even in terms of 3 year returns equity mutual funds in India have outperformed fixed deposits from banks.
Past track record no indication of future performance
Just because the returns from equity mutual funds has been solid over the last few years, it does not mean they will outperform bank deposits in the future.
A few important things must also be said. The out performance of mutual funds has largely been on the back of a solid rally in stocks in the last one year on account of hopes from the Narendra Modi government.
So, what returns one is seeing in the above table is on account of the solid returns in the last one year. If we take the last one year returns out, there may not be much to talk about in terms of out performance of equity mutual fund schemes.
Secondly, the rally is come on the back of quantitative easing across the globe from Japan to the EU. We are likely see an interest rate hike in the US shortly and things may not be conducive for equities as they have been in the last one year.
Hence, past track record of mutual funds is no indication of future performance. To expect returns in the range of 20-25 per cent as in the past maybe a little far fetched. It's best to tone down expectations and expect reasonable returns and not stupendous returns.
Hence to say equity mutual funds will give better returns that bank deposits maybe a little difficult to call since equities have run up too fast.
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