a bank loaned out $17000, part of it at the rate of 8% per year and the rest at 18% per year.

Question

a bank loaned out $17000, part of it at the rate of 8% per year and the rest at 18% per year. If the interest received in one year totaled $2,500, how much was loaned at 8%?

Answer 1

First Set Variables: 

 

x = Total Dollar Amount loaned at 8%

 

y = Total Dollar Amount loaned at 18%

 

so, 

 

x + y = $17,000

 

 

Next, Set up overall Equation for the Interest: 

 

$2,500 = 0.08*x + 0.18*y

 

 

Substitute for Y, in terms of X:

 

2,500 = (0.08*x + 0.18* (17,000-x))

 

 

--Finally, Solve for X (the amount loaned at 8%)

 

Answer 2

Let  $'x' be the amount loaned at 8%, the amount loaned at 18% will be $(17000-x)

 

Total interest = x*8/100  +  (17000-x) * 18/100

 

2500 = 0.8x + 3060 - 1.8x

 

2500 = 3060 - x

 

So, x = 3060 - 2500

 

x = $ 560 i.e. amount loaned at 8%