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Math Help - Simple interest question

  1. #1
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    Simple interest question

    A company invests $50000, some into an account paying 5.2% per annum simple interest and the remainder in an account paying 4.5% simple interest per annum. After 2 years the $50000 had grown to $54976. How much went into each account?

    What is the formula for this type of question? I worked it out by trial and error, but I know that this isnt the right way.

    Thanks
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Local_lunatic View Post
    A company invests $50000, some into an account paying 5.2% per annum simple interest and the remainder in an account paying 4.5% simple interest per annum. After 2 years the $50000 had grown to $54976. How much went into each account?

    What is the formula for this type of question? I worked it out by trial and error, but I know that this isnt the right way.

    Thanks
    Recall that Simple Interest = Principle * Rate * Time

    The interest gained here is, of course, 54976 - 50000 = 4976

    So now we set up our simple interest equations. we have two accounts, so we must have a sum of the two simple interests giving 4976

    Thus we have: Principle_1 * Rate_1 * Time + Principle_2 * Rate_2 * Time = 4976

    so let's say the first account is the one that gives 5.2% interest. And let's say we invest x dollars into this account. what do we have remaining? well, (50000 - x) dollars, of course.

    so our equation becomes:

    x*5.2 \% * 2 + (50000 - x)*4.5 \% *2 = 4796

    or 2(0.052)x + 2(0.045)(50000 - x) = 4796

    now solve for x, that will be the amount you invested into the first account. then subtract that answer from 50000 to find how much you invested into the second account
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    Recall that Simple Interest = Principle * Rate * Time

    The interest gained here is, of course, 54976 - 50000 = 4976

    So now we set up our simple interest equations. we have two accounts, so we must have a sum of the two simple interests giving 4976

    Thus we have: Principle_1 * Rate_1 * Time + Principle_2 * Rate_2 * Time = 4976

    so let's say the first account is the one that gives 5.2% interest. And let's say we invest x dollars into this account. what do we have remaining? well, (50000 - x) dollars, of course.

    so our equation becomes:

    x*5.2 \% * 2 + (50000 - x)*4.5 \% *2 = 4796

    or 2(0.052)x + 2(0.045)(50000 - x) = 4796

    now solve for x, that will be the amount you invested into the first account. then subtract that answer from 50000 to find how much you invested into the second account
    That's basically where I managed to get to except that I simplified it down a bit more.

    0.104x + 0.09(50000 - x) = 4796

    or 0.052x + 0.045(50000 - x) =2398

    How would I go about solving it for x though?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Local_lunatic View Post
    That's basically where I managed to get to except that I simplified it down a bit more.

    0.104x + 0.09(50000 - x) = 4796

    or 0.052x + 0.045(50000 - x) =2398

    How would I go about solving it for x though?
    your second line profited nothing.

    do you know how to expand brackets?

    2(0.052)x + 2(0.045)(50000 - x) = 4796

    \Rightarrow 0.104x + 0.09(50000 - x) = 4796

    now we expand the brackets for the second term. we take the 0.09 and multiply each term in the brackets one at a time

    \Rightarrow 0.104x + 0.09(50000) + 0.09(-x) = 4796

    \Rightarrow 0.104x + 4500 - 0.09x = 4796

    now add the x's

    \Rightarrow 0.014x + 4500 = 4796

    Can you take it from here?
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  6. #6
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    So from the beginning

    2(0.052)x + 2(0.045)(50000-x) = 4976

    0.104x + 0.09(50000-x) = 4976

    0.104x + 4500 - 0.09x = 4976

    0.104x-0.09x = 4976 - 4500

    0.014x = 476

    476 / 0.014 = 34000

    50000 - 34000 = 16000

    Account 1(x) =$34000
    Account 2 =$16000


    Here's another one.

    Junior invests $4000, some into an account paying 6.5%pa simple interest and the remainder into an account paying 5.8%pa simple interest. After 18months the $4000 has grown to $4391.60. How much did Junior put into each account?

    1.5(0.065)x + 1.5(0.058)(4000-x) = 381.6

    0.0975x + 0.087(4000-x) = 381.6

    0.0975x + 348 - 0.087x = 381.6

    0.095x - 0.087x = 381.6 - 348

    0.0105x = 33.6

    33.6 / 0.0105 = 3200

    4000-3200 = 800

    Account 1(x) = $3200
    Account2 = $800

    Have I done these right?
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Local_lunatic View Post
    So from the beginning

    2(0.052)x + 2(0.045)(50000-x) = 4976

    0.104x + 0.09(50000-x) = 4976

    0.104x + 4500 - 0.09x = 4976

    0.104x-0.09x = 4976 - 4500

    0.014x = 476

    476 / 0.014 = 34000

    50000 - 34000 = 16000

    Account 1(x) =$34000
    Account 2 =$16000


    Here's another one.

    Junior invests $4000, some into an account paying 6.5%pa simple interest and the remainder into an account paying 5.8%pa simple interest. After 18months the $4000 has grown to $4391.60. How much did Junior put into each account?

    1.5(0.065)x + 1.5(0.058)(4000-x) = 381.6

    0.0975x + 0.087(4000-x) = 381.6

    0.0975x + 348 - 0.087x = 381.6

    0.095x - 0.087x = 381.6 - 348

    0.0105x = 33.6

    33.6 / 0.0105 = 3200

    4000-3200 = 800

    Account 1(x) = $3200
    Account2 = $800

    Have I done these right?
    it should be 1.5(0.065)x + 1.5(0.058)(4000-x) = \color {red}391.6

    but you're setup looks correct. work out the answer with the corrected RHS
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  8. #8
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    My bad, the question was meant to be $4381.60 instead of $4391.60. Thanks for helping me understand it
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