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?
was loaned at 15% and
was loaned at 6%
Let's let x represent the amount loaned at 15% and y represent the amount loaned at 6%.
We know that the total amount loaned out was $7,500, so we can write the equation:
x + y = 7500
We also know that the total interest earned for both loans was $540, so we can write the equation:
0.15x + 0.06y = 540
Let's solve this system of equations to find the values of x and y.
To eliminate y, we'll multiply the first equation by -0.06 and the second equation by 100 to get rid of the decimal points:
-0.06x - 0.06y = -450
15x + 6y = 54000
Now we can add the equations together:
-0.06x - 0.06y + 15x + 6y = -450 + 54000
14.94x = 53550
Dividing both sides by 14.94, we get:
x = 3583.12
Substituting this value back into the first equation, we can solve for y:
3583.12 + y = 7500
y = 7500 - 3583.12
y = 3916.88
Therefore, $3,583.12 was loaned at 15% and $3,916.88 was loaned at 6%.