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I have 7000$ invested in annuity, part at a yearly rate of 9% and part at a yearly rate of 11%. The total interest earned for one year is $654. How much was invested at each rate?

Answer :

$5800 at 9%
$1200 at 11%

0.09(x) = interest earned at 9%
0.11(7000-x) = interest earned at 11%

0.09(x) + 0.11($7000-x) = $654
0.09x + $770 - 0.11x = $654
$770 - $654 = 0.11x - 0.09x
$116 = 0.02x
$116/0.02 = x
$5800 = x

$5800 * 0.09 = $522

($7000-$5800) * 0.11 = $132


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