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alexandr1967 [171]
2 years ago
11

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 on

e year is $654. How much was invested at each rate?
Mathematics
1 answer:
makvit [3.9K]2 years ago
7 0
$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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You can do this through synthetic division. It is a shorthand way of dividing polynomials.

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x⁵ - x³ + (-5)   →  x⁵ + 0x⁴- x³ + 0x² + 0x + (-5)

Now you can proceed to synthetic division. Make an upside down division box with the divisor outside and the coefficients of the dividend listed, along with their sign. Leave a space below the divident

+2 |   +1     0     -1     0     0     -5

    |<u>                                              </u>

Next you bring down the first coefficient:

+2 |   +1     0     -1     0     0     -5

    |<u>                                              </u>

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Then you multiply it by the divisor and write the product under the next coefficient:

+2 |   +1     0     -1     0     0     -5

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Next add the column and put the sum below it:

+2 |   +1     0     -1     0     0     -5

    |<u>          +2                                   </u>

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Then multiply again and repeat until you reach the last coefficient:

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Now the last coefficient is your remainder. So your results will be:

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