Problema Solution
A bank loaned out $120,000, part of it at the rate of 8% per year and the rest at the rate of 12% per year. If yhe interest recieved totaled $11,000, how much was loaned at 8%? Show how you came to your calculation.
Answer provided by our tutors
Since the bank lent out two amounts, substitute x for one of the amounts. It doesn't matter which one. First amount is x and second amount is (120,000-x).
We know that the principal multiplied by the rate of interest will give us the interest. First amount is x multipied by 8% or .08. That interest is equal to .08x. Second amount is (120,000-x) multiplied by 18% or .18. That interest is equal to .18(120,000-x). Since you know that the interest from both amounts is equal to 10,000, you can set up your equation as
.08x+.18(120,000-x)=10,000 then solve for x.
.08x + 21600-.18x=10000
-.10x+21600=10000
-.10x+21600-21600=10000-21600
-.10x=-11600
x=116,000
Second equation is 120,000-116,000. That is equal to 4,000.
So, 116,000 was lent at 8% and 4000 at 18%. The combined interest from these amounts equals 10,000.