Question

A bank loaned out $27,000, part of it at the rate of 11% annual interest, and the rest at 12% annual interest. The total interest earned for both loans was $3,075.00. How much was loaned at each rate?

Answer 1

The bank loaned out $16,500 at a rate of 11% annual interest and $10,500 at a rate of 12% annual interest.

Step-by-step explanation:

Let x be the amount loaned at 11% interest and y be the amount loaned at 12% interest. We can set up two equations to represent the given information:

x + y = 27000

0.11x + 0.12y = 3075

We can solve this system of equations using the substitution method:

1. Rearrange the first equation to solve for x: x = 27000 - y
2. Substitute the value of x in the second equation: 0.11(27000 - y) + 0.12y = 3075
3. Simplify and solve for y: 2970 - 0.11y + 0.12y = 3075
   0.01y = 105
   y = 10500
4. Substitute the value of y back into the first equation to solve for x: x + 10500 = 27000
   x = 16500

Therefore, $16,500 was loaned at a 11% interest rate and $10,500 was loaned at a 12% interest rate.