A bank loaned out $23,500, part of it at the rate of 14% annual interest, and the rest at 5% annual interest. The total interest earned for both loans was $1,625.00. How much was loaned at each rate?

Answer 1

Let x be the amount loaned at 14% annual interest.
The amount loaned at 5% annual interest is 23500 - x.
The interest earned from the 14% loan is x * 0.14.
The interest earned from the 5% loan is (23500 - x) * 0.05.
The total interest for both loans is x * 0.14 + (23500 - x) * 0.05.
We know that x * 0.14 + (23500 - x) * 0.05 = 1625.
Multiplying through the parentheses, we get 0.14x + 1175 - 0.05x = 1625.
Combining like terms, we get 0.09x + 1175 = 1625.
Subtracting 1175 from both sides, we get 0.09x = 450.
Dividing both sides by 0.09, we get x = 5000.
The amount loaned at 14% annual interest is 5000.
The amount loaned at 5% annual interest is 23500 - 5000 = 18500. Answer: \boxed{5000, 18500}.