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Math Help - Grade 11 Math Problems

  1. #1
    Junior Member VDestinV's Avatar
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    Exclamation Grade 11 Math Problems

    I need to get these two questions fully understood so could someone please answer them and explain thank you.

    1) Madeleine works at a company that offers bonuses to its employees, depending on their performance. Madeleine is offered the choice of recieving four cheques of $300, one every 3 months throughout the year, or waiting until the end of the year and recieving a single cheque of $1300. Madeleine finds out that the highest interest rate offered by the banks os a guaranteed rate of 7.5% interest compounded quareterly. Illustrate Madeleine's choices using a timeline, to help her decide which bonus offer to accept.


    2) Would you make more money by investing $100 a month at 12% interest compounded monthly for 5 years or by investing $1200 a year at 12% interest compounded annually for 5 years?
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  2. #2
    Junior Member VDestinV's Avatar
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    Forget about #2 I figured it out
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  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by VDestinV View Post
    I need to get these two questions fully understood so could someone please answer them and explain thank you.

    1) Madeleine works at a company that offers bonuses to its employees, depending on their performance. Madeleine is offered the choice of recieving four cheques of $300, one every 3 months throughout the year, or waiting until the end of the year and recieving a single cheque of $1300. Madeleine finds out that the highest interest rate offered by the banks os a guaranteed rate of 7.5% interest compounded quareterly. Illustrate Madeleine's choices using a timeline, to help her decide which bonus offer to accept.


    2) Would you make more money by investing $100 a month at 12% interest compounded monthly for 5 years or by investing $1200 a year at 12% interest compounded annually for 5 years?
    We will need the formlula

    A=A_0\left( 1+\frac{r}{n}\right)^{nt} where r is the interest rate and n is the number times compounded per year and t is time (in years)

    I'm guessing this is what you mean at time t=0 she gets 300 then in three months she gets 300 more,... so after nine months the company has given her $1200 dollars we want to know if she can make more money if she takes this option then the $1300 lump sum.

    We know that A_0=300 \\\ r=0.075 \\\ n=4 so we get

    A=300(1+\frac{0.075}{4})^{4t}

    We need to find out how much money she has after 3 months so (1/4 of a year) so we get

    A=300(1+\frac{0.075}{4})^{4\cdot \frac{1}{4}}=305.625

    But now she gets another 300 from here company and invests it for another 3 months to get

    A=(300+305.625)(1+\frac{0.075}{4})^{4\cdot \frac{1}{4}}=616.98

    again she gets 300 more so at 9 months she has


    A=(300+616.98)(1+\frac{0.075}{4})^{4\cdot \frac{1}{4}}=934.91

    one more time to get for the year

    A=(300+934.91)(1+\frac{0.075}{4})^{4\cdot \frac{1}{4}}=1257.31

    So it is better to take the 1300 at the end of the years
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