Question

a bank loaned out $20,000, part of it at the rate of 14% annual interest, and the rest at 3% annual interest. the total interest earned for both loans was $985.00. how much was loaned at each rate?

Answer 1

To solve for the amounts loaned at each interest rate, a system of linear equations is set up with two unknowns representing the amounts at 14% and 3% interest rates. By applying system-solving techniques, it was found that $3,500 was loaned at 14% interest and $16,500 at 3% interest.

Step-by-step explanation:

To determine how much was loaned at each interest rate given a total loan amount of $20,000 and a total interest of $985, we can set up a system of linear equations. Let's denote the amount loaned at 14% annual interest as x and the amount loaned at 3% annual interest as y. We have two conditions:

• The sum of the amounts loaned at both rates is $20,000: x + y = 20,000.
• The total interest from both loans is $985: 0.14x + 0.03y = 985.

We can use substitution or elimination to solve this system. If we subtract the second equation from the first one multiplied by 0.03, we eliminate y and can find the value of x. Then we can substitute the value of x back into any of the equations to find y.

Here's how the calculations would look:

1. Multiply the first equation by 0.03: 0.03x + 0.03y = 600.
2. Subtract this from the second equation: 0.14x - 0.03x + 0.03y - 0.03y = 985 - 600.
3. Simplify and solve for x: 0.11x = 385, thus x = 385 / 0.11, which gives x = $3,500.
4. Substitute x into the first equation: 3,500 + y = 20,000, thus y = 20,000 - 3,500, which gives y = $16,500.

So, $3,500 was loaned at 14%, and $16,500 was loaned at 3% annual interest.

Answer 2

The bank loaned out $3,500 at a 14% annual interest rate, and $16,500 at a 3% annual interest rate.

Step-by-step explanation:

Let's assume that the amount loaned at 14% annual interest is x dollars.

Therefore, the amount loaned at 3% annual interest is $20,000 - x dollars.

Now we can set up an equation based on the information given:

1. 0.14x + 0.03($20,000 - x) = $985

Simplifying the equation, we get:

1. 0.14x + $600 - 0.03x = $985
2. 0.11x = $385
3. x = $3,500

Therefore, $3,500 was loaned out at a 14% annual interest rate, and $16,500 was loaned out at a 3% annual interest rate.