A bank loaned out $20,500, part of it at the rate of 13% annual interest, and the rest at 8% annual interest. The total interest earned for both loans was $2,015.00. How much was loaned at each rate?

Answer 1

Let x be the amount the amount loaned at 13%

We would write it as x(1+.13)=x(1.13)

Let y be the amount loaned at 8%

So y(1+.08)=y(1.08)

x+y=20500

Subtracting x from both sides

y=20500-x

Principal plus Interest is 20500+2015=22515

x(1.13)+y(1.08)=22515

Substitute in place of y

x(1.13)+(20500-x)(1.08)=22515

1.13x+22140-1.08x=22515

Combine x's and subtract 22140 from both sides

.05x=-375

Divide both sides by .05

x=$7500

Since y=20500-x=20500-7500=13000

The amount loaned at 13% is $7,500 and the amount loaned at 8% is $13,000

To check:

7500(.13)=975

13000(.08)=1040

975+1040=2015 the total interest