Need help with Annualized Return

Hi
It would be great if someone can help me with the formula of annualized returns

Is it (1+r%)^ (days/365) -1 or (1+r%)^ (365/days)-1

I never seem to get it right

If r is the effective rate for days, then the (effective) annual rate is:

\left(1 + r\right)^{\frac{365}{days}} - 1

If r is the effective annual rate, then the effective rate for days is:

\left(1 + r\right)^{\frac{days}{365}} - 1

For example, if you earn a 2% return in 175 days, the effective annual rate is:

1.02^{\left(\frac{365}{175}\right)} - 1 = 4.2167\%

If the effective annual rate is 4.5%, then the effective 120-day rate is:

1.045^{\left(\frac{120}{365}\right)} - 1 = 1.4577\%
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