SOLUTION: a bank loaned out 11,500, part of its interest rate of 7% annual interest, and the rest at 13% interest annual interest. the total interest earned for both loans was 865.00. how mu
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Question 1155462: a bank loaned out 11,500, part of its interest rate of 7% annual interest, and the rest at 13% interest annual interest. the total interest earned for both loans was 865.00. how much was loaned at each rate? Answer by ikleyn(52769) (Show Source):
Let x = amount loaned at 13%.
The the amount loaned at 7% is (11500-x) dollars.
Annual interest produced by the first amount is 0.13x dollars.
Annual interest produced by the first amount is 0.07*(11500-x) dollars.
The total interest of 865 dollars is the sum of partial amounts
0.13x + 0.07*(11500-x) = 865.
From this equation
x = = 1000.
ANSWER. $1000 was loaned at 13%, and the rest 11500-1000 = 10500 dollars were loaned at 7%.
CHECK. 0.13*1000 + 0.07*10500 = 865 dollars. ! Precisely correct !
Solved.
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It is a standard and typical problem on investments.
You will find there different approaches (using one equation or a system of two equations in two unknowns), as well as
different methods of solution to the equations (Substitution, Elimination).
