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Juan borrows $100,000 to pay for medical school. He borrows part of the money from the school whereby he will pay 4.5% simple interest. He borrows the rest of the money through a government loan that will charge him 6% interest. In both cases, he is not required to pay off the principal or interest during his 4 yr of medical school. However, at the end of 4yr, he will owe a total of $19,200 for the interest from both loans. How much did he borrow from each source?

Respuesta :

CastleRook
let the amount Juan borrows from the from school be x, and the amount borrowed in government be y.
Total amount of money will be:
x+y=100,000
x=100,000-y......i
given that the interest charged from the money is simple interest, the amount of interest charged from x will be:
interest=(PRT)/100
=(x×4.5×4)/100
=0.18x

interest charged in y will be:
(y×6x4)/100
=0.24y
therefore the total interest will be:
0.18x+0.24y=19200.....ii
substituting i in ii we get:
0.18(100000-y)+0.24y=19200
18000-0.18y+0.24y=19200
0.24y-0.18y=19200-18000
0.06y=1200
y=1200/0.06
y=20,000
x=10000-20000
x=80,000
therefore he borrowed $80,000 from school and $20,000 from government. 

 

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