A bank loaned out $7,500, part of it at the rate of 15% annual interest, and the rest at 6% annual interest. The total interest earned for both loans was $540.00. How much was loaned at each rate?
Let x be the amount loaned at 15% interest.
Therefore, the amount loaned at 6% interest is 7500 - x.
The interest earned from the loan at 15% interest is 0.15x.
The interest earned from the loan at 6% interest is 0.06(7500 - x).
We know that the total interest earned for both loans is $540.00, so:
0.15x + 0.06(7500 - x) = 540
0.15x + 450 - 0.06x = 540
0.09x + 450 = 540
0.09x = 90
x = 1000
Therefore, $1000 was loaned at 15% annual interest, and $6500 was loaned at 6% annual interest. Answer: \boxed{1000, 6500}.