Equation below assumes equal time periods

(1 + S1) x (1 + S2) x ... (1 + Sn) - 1

((1+.004) * (1+.0019) * (1+.0018)) - 1 = .007718 = .77%

What would be the equation/formula for unequal time period returns using the equation above to get a time weighted return?

for example:

.004 for 10 days

.0019 for 30 days

.0018 for 50 days.

Analysis period 90 days.

Trying to time weight the individual returns within this formula or any suggestion.

A test of any suggestion would be to enter an equal weighting for each variable with the result being .007718 = .77%; the same as the first equation where variables are defined as being weighted equally.

Am completely new to forums and am not familiar with etiquette; however, I would expect to pay for work done correctly; just don't know procedure.