If you post a sample calculation (with real or fictitious numbers), I will review it. I think we can resolve any issues. I should be able to explain to you how to perform the calculation you describe.
From your post, I think one of the issues may be in determining the daily dividend rate.
For example, if the yearly rate is 5% the daily rate (in %) is not .05/366; but, is the 366th root of 1.05 less 1 times 100. This sounds more complicated than it really is.
For an aggregate yearly rate of 5.58%, the daily rate is 0.0148%.
To go from the daily rate to the yearly rate follow these steps.
1) express the daily rate as a decimal .000148
2) add 1 1.00148
3) raise this number to the 366th power (leap year) 1.0558
4) subtract 1 and multiply by 100 5.58%
The main trick is to remember that TIAA quotes compound annual rates, not simple interest rates. Also, when using data from one day - the round off errors can be significant. An accumulation of $3001.00 can actually be any number between $3000.9950 and $3001.0049. When this number is compounded by the number of days in the year the error also grows.
Jack