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It looks like you got credit for the money being at Vanguard for 14 days. This is how you can calculate it.
3000*.00435= 13.05
Divided by 31(days in month) 13.05/31 = .42096
Times number of days Vanguard had money.42096*14= 5.89
The difference is probably in the .00435 starting figure. They may also use a 360 or 365 day year to calculate interest this will also make a difference.
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