Question

Mr. jackson borrowed money from his bank and on his life insurance to start a business. his interest rate on the bank loan was 10%, and his rate on the insurance loan was 12%. if the total amount borrowed was $100,000 and his total yearly interest payment was $10,900, how much did he borrow from the bank? $

Answer 1

Let X be the amount borrowed from the bank and Y be the amount borrowed from the life insurance.

 

X + Y = 100,000  

as he borrowed $100,000

 

0.10X + 0.12Y = 10900  

10% = 0.10 and 12% = 0.12;  

The total interest is $10,900

 

Solving the first equation for Y and multiplying the second equation by 100 to clear the decimals:

 

Y  = 100,000 - X

 

10X + 12Y = 1090000

 

Plugging the first equation into the second:

 

10X + 12(100,000 - X) = 1090000

 

10X + 1200000 - 12X = 1090000 -------- distributive property

 

 

0 = 12X - 10X + 1090000 - 1200000  --- moves everything to right side, signs change; like to keep coefficient positive

 

0 = 2X -110000  --- combines like terms

 

110000 = 2x ---- solves for X

 

110000/2 = X --- adds 180000 to both sides; then divides by 4

 

X = 55000

 

Y = 100000 - 55000 = 45000

 

CHECK:  55000 x 10% + 45000 x 12% = 55000 x 0.10 + 45000 x 0.12  

= 5500 + 5400 = 10,900

 

He borrowed 55000 from the bank and 45000 from the insurance.