A bank loaned out $21,000, part of it at the rate of 3% annual interest, and the rest at 14% annual interest. The total interest earned for both loans was $960.00. How much was loaned at each rate?
Answers
21000(P) = 2215
P = 0.1055 or 10.55 %
This number is a weighed average of the 4% yield and the 15% yield so the next equation to solve is
10.55 = 4(1 – X) + 15X
Where X is the proportion of the loan given at the indicated interest. So
10.55 = 4 – 4X + 15X
6.55 = 11X
X = 0.5955
1-X = 0.4045
So the portion of the loan lent @ 4% is 21000(0.5955) = $12,505.5
And the portion of the loan lent @ 15% is 21000(0.4045) = $8494.5
$8500 at 4%
12500 at 15%
A system of two equations in two unknowns, x and y will work here
x = amount loaned at 4%
y = amount loaned at 15%
Equation 1 for total amount of loan
x + y = 21000
Equation 2 for total interest based on the rates
0.4x + 0.15y = 2215
I will the Substitution Method with Equation 1 to solve the problem
x + y = 21000
y = 21000 - x
Substitute this quantity into Equation 2 for y
0.04x + 0.15y = 2215
0.04x + .15(21000 - x)
0.04x + 3150 - 0.15x = 2215
Combine like terms
-0.11x + 3150 = 2215
Subtract 3150 from both sides of the equation
-0.11x = -935
Divide both sides by -0.11x
x = 8500
y = 21000 - 8500
y = 12500
Checking with Equation 2
0.04x + 0.15y = 2215
0.04(8500) + 0.15(12500) = 2215
340 + 1875 = 2215
2215 = 2215