A bank loaned out $21,000, part of it at the rate of 4% annual interest, and the rest at 15% annual interest. The total earned for both loans was $2,215.00. How much was loaned at each rate?

Answer 1

This problem can be solved in several ways. The way I like is as follows.

Ask yourself at what interest would $ 21,000 yield and interest of $ 2,215 in one year ? The equation to solve is:

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

Answer 2

$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

I hope you find this useful if you have any questions send me a message.