Question 234701
The formula for simple interest is
{{{A = P*(1 + rt)}}}
{{{A}}} = amount after {{{t}}} years
{{{r}}} = interest rate
{{{P}}} = original amount
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Let {{{x}}} = amount loaned by 1st bank
Then {{{12000 - x}}} will be the amount loaned by other bank
bank 1:
{{{r = .075}}}
{{{P[1] = x}}}
{{{A[1] = x*(1 + .075*1)}}}
{{{A[1] = 1.075x}}}
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bank 2:
{{{r = .09}}}
{{{A[2] = (12000 - x)*(1 + .09*1)}}}
{{{A[2] = 1.09*(12000 - x)}}}
{{{A[2] = 13080 - 1.09x}}}
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The interest paid to bank 1 is {{{A[1] - P[1]}}}
The interest paid to bank 2 is {{{A[2] - P[2]}}}
The total interest paid to the two banks is
{{{(A[1] + A[2]) - (P[1] + P[2])}}}
The total interest paid is $960
{{{(A[1] + A[2]) - (x + 12000 - x) = 960}}}
{{{1.075x + 13080 - 1.09x - 12000 = 960}}}
{{{-.015x + 1080 = 960}}}
{{{-.015x = -120}}}
{{{x = 8000}}}
{{{12000 - x = 12000 - 8000}}}
{{{12000 - x = 4000}}}
$8000 was loaned at bank 1
$4000 was loaned at bank 2
check answer:
{{{A[1] = x*(1 + .075*1)}}}
{{{A[1] = 8000*1.075}}}
{{{A[1] = 8600}}}
and
{{{A[2] = 1.09*(12000 - x)}}}
{{{A[2] = 1.09*4000}}}
{{{A[2] = 4360}}}
and
{{{(A[1] + A[2]) - (P[1] + P[2]) = 960}}}
{{{8600 + 4360 - 8000 - 4000 = 960}}}
{{{12960 - 12000 = 960}}}
{{{960 = 960}}}
OK