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Jenny borrowed a total of 20,000 from two different banks to start a business. One bank charged the equivalent of 6% simple interest, and the other charged 4.5% interest. If the total interest after 2 years was $2340, determine the amount borrowed from each bank.

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danialamin

Answer:

Jenny has borrowed $18000 from bank 1 and $2000 from bank 2.

Explanation:

The simple interest is given as

[tex]I=P(1+rn)-P[/tex]

Here

I is the interest value

P is the principle amount

r is the rate of interest

n is the number of years

Let the amount borrowed from the first bank is X while that of second bank is Y thus

Interest for bank 1 is given as

[tex]I_1=X(1+rn)-X\\I_1=X(1+2(6\%))-X\\I_1=X(1+0.12)-X\\I_1=1.12X-X[/tex]

So the interest for the second bank is given as

[tex]I_2=Y(1+rn)-Y\\I_2=Y(1+2(4.5\%))-Y\\I_2=Y(1+0.09)-Y\\I_2=1.09Y-Y[/tex]

As per the given condition

[tex]I_1+I_2=2340\\[/tex]

So the equation becomes

[tex]1.12X-X+1.09Y-Y=2340[/tex]

This is simplified as

[tex]0.12X+0.09Y=2340[/tex]

Also the total money borrowed is given as 20,000  thus

[tex]X+Y=20000[/tex]

Solving these two equations result in

X=18000, Y=2000

So Jenny has borrowed $18000 from bank 1 and $2000 from bank 2.

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