Abank loaned out $17,000, part of it at the rate of 14% annual interest, and the rest at 9% annual interest. the total interest earned for both loans was $2,180.00. how much was loaned at each rate?

$4,000 ⇒ amount invested at 9% and $13,000 ⇒ amount invested at 14%.

Explanation:

Given that,

Bank loaned out = $17,000

Part of it loaned at annual interest rate(r1) = 14%

Interest rate on remaining(r2) = 9%

Total interest earned for both loans was $2,180

Let amount invested at rate of 9% be x,

(r2)x + r1(Total loaned amount - x) = Total interest earned

0.09x + 0.14(17,000 - x) = 2,180

  0.09x + 2,380 - 0.14x = 2180

                            0.05x = 200

                                   x = $4,000 ⇒ amount invested at 9%

Therefore,

17,000 - x ⇒ 17,000 - 4,000 = $13,000 ⇒ amount invested at 14%