A bank loaned out $17,500, part of it at the rate of 4% annual interest, and the rest at 9% annual interest

Question

A bank loaned out $17,500, part of it at the rate of 4% annual interest, and the rest at 9% annual interest. The total interest earned for both loans was $1,100.00. How much was loaned at each rate?

Answer 1

Ok, so we know the bank loaned part of the $17,500 at a 4% interest rate.  Lets call this loan amount x.  Then the rest of the 17,500 was loaned at a 9% interest rate.  Whatever this amount was, we can define it as 17,500 - x.  We also know that the total interest earned was $1,100.  With this information, we can form the following equation:

 

.04(x) + .09(17500 - x) = 1100

Multiply the .09 times the inside of the parentheses:

.04x + 1575 - .09x = 1100

Simplify:

-.05x + 1575 = 1100

-.05x = -475

x = 9500

 

Since x is originally the amount loaned at the 4% interest rate, we know that $9,500 was loaned at a 4% interest rate.

 

To figure out the other amount loaned at 9%, simply subtract 9,500 from 17,500 -- this gets us 8,000.  So $8,000 was loaned at a 9% interest rate.

 

I hope this helps!