interest rate

Question

To get the necessary funds for a planned expansion, a small company took out three loans totaling $21,000. Company owners were able to get interest rates of 6%, 7%, and 8%. They borrowed $1000 more at 7% than they borrowed at 8%. The total annual interest on the loans was $1390.

How much did they borrow at each rate?

The company borrowed $___ at 6%, $___ at 7%, and $___ at 8%

Answer 1

The amounts are X,Y,and Z respectively with Y = Z+1000.

 

X+(Z+1000)+Z= 21000

 

 

X+ 2Z + 1000 = 21000

 

X+ 2Z = 20000 ---> X = 20000 - 2Z

 

 

0.06X + 0.07Y + 0.08Z  = 1390

 

0.06X + 0.07(Z+1000) + 0.08Z = 1390

 

0.06X + 0.07Z + 70 + 0.08Z  = 1390

 

0.06X + 0.15Z = 1320

 

6X + 15Z = 132000

 

6(20000 - 2Z) + 15Z = 132000

 

120000 - 12Z + 15Z = 132000

 

120000 + 3Z = 132000

 

3Z = 132000 - 120000  

 

3Z = 12000

 

Z = 4000

 

X = 12000

 

Y = 5000

 

CHECK:

0.06*12000 + 0.07*5000 + 0.08*4000 = 1390