Personal rate of return calculation question?

Thanks in advance.

What exactly is one's personal rate of return? Is it the internal rate of return?

e.g.
A mutual fund's prospectus states that it had an annual rate of return of 10% over the past year. I assume that return was calculated assuming that:
- A person made a one time lump sum investment Jan. 1st
- Did not invest any more or sell any shares
- Held their position until Dec. 31st

If no dividends or capital gains is the return simply calculated as below?
|starting NAV - ending NAV| / (starting NAV) * 100

Is using the IRR a better way of calculating your "true" return because it takes into account your added investments?

e.g.
Min. investment is $1k, you add $100 monthly (including Jan) and the fund's balance Dec. 31st is $2200, was your return 0%?

I am trying to ask how to extrapolate your contributions vs. market value change in calculating your rate of return (even though they are coupled by way of buying more shares with your contributions).

Ypu also need to take into account brokers fees, taxes, and if a mutual fund the load they charge. Then you have you ror