Question

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.

Answer 1

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

Step-by-step explanation:

The simple interest is given as

`I=P(1+rn)-P`

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

`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`

So the interest for the second bank is given as

`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`

As per the given condition

`I_1+I_2=2340\\`

So the equation becomes

`1.12X-X+1.09Y-Y=2340`

This is simplified as

`0.12X+0.09Y=2340`

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

`X+Y=20000`

Solving these two equations result in

X=18000, Y=2000

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