Question

A bank loaned out $27,000, part of it at the rate of 8% annual interest, and the rest at 5% annual interest. The total interest earned for both loans was $1,890.00. How much was loaned at each rate?

a) $12,000 at 8%, $15,000 at 5%
b) $15,000 at 8%, $12,000 at 5%
c) $10,000 at 8%, $17,000 at 5%
d) $17,000 at 8%, $10,000 at 5%

Answer 1

By solving the system of equations, we found that $15,000 was loaned at 8% interest and $12,000 was loaned at 5% interest. The correct answer is b) $15,000 at 8%, $12,000 at 5%.

Thus, the correct option is B.

Step-by-step explanation:

To solve the problem regarding how much was loaned at each interest rate by the bank, we need to set up a system of equations based on the information provided:

1. The total amount loaned out was $27,000.
2. Part was loaned at 8% interest, and the rest at 5% interest.
3. The total interest earned from both loans was $1,890.

Let's use x to represent the amount loaned at 8% interest, and y to represent the amount loaned at 5% interest. We can then establish the following equations:

• x + y = 27,000 (since the total amount loaned out was $27,000)
• 0.08x + 0.05y = 1,890 (representing the total interest from both loans)

Solving this system of equations, we get:

• x = $15,000 loaned at 8%
• y = $12,000 loaned at 5%

Therefore, the correct answer is b) $15,000 at 8%, $12,000 at 5%.