a bank loaned out $21,500, part of it at the rate of 4% annual interest, and the rest at 9% annual interest. The total interest earned for both loan was $1,085.00. How much was loaned at each rate?

Answer 1

Since we the question doesn't specify $1,085.00 was the interest earned after how many years, let me assume it's the interest earned after 1 year.

We have this equation:

Total interest earned = $1,085 = a * 4% + b * 9% (equation 1)

At the same time we know that a + b = $21,500 => a = $21,500 - b => plug this in equation 1 we have:

$1,085 = a * 4% + b * 9%

<=> $1,085 = ($21,500 - b)* 4% + b * 9% => you can find b value based on this equation, and then a.