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The difference is the compounding:
- The first one assumes the 8% rate has an annual compounding, I.e., the 8% is only counted in a 1-year interval. This is the simplest way
- The second one assumes the 8% is compound quarterly. This means, each quarter produces the (1+.08)^(1/4) - 1 rate, which means every quarter counts that
The difference in practice is that when you compound quarterly, in the second quarter you will have "an interest over the previous interest".
For you to know which one is correct, you need to know the compound period... There's no other way. Ofc, you need to evaluate whether or not this additional precision is really needed, but mathematically, that's it
Bingo, Bango, Dodge Durango
Example, Capital Balance is $1,259,086 and preferred return rate is 8%
1,259,086 * 8/4 = 25,182
1,259,086 * (1+.08)^(1/4) - 1,259,086 = 24,460