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Math Help - Compound interest : Present value

  1. #1
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    Compound interest : Present value

    Sally invests some money at 6%/a compounded annually. After 5 years, she takes the prinicpal interest and reinvests it all at 7.2%/a compounded quarterly for 6 more years.At the end of this time, her investment is worth $14784.56. How much did sally originally invest ?
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  2. #2
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    Re: Compound interest : Present value

    Hello, darkangel06!

    I must assume that you know the Compound Interest Formula.

    . . A \;=\:P(1 + i)^n\;\;\text{ where: }\:\begin{Bmatrix}P &=& \text{principal invested} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods}\end{Bmatrix}


    Sally invests some money at 6%/a compounded annually.
    After 5 years, she takes the prinicpal and interest and reinvests it all
    . . at 7.2%/a compounded quarterly for 6 more years.
    At the end of this time, her investment is worth $14784.56.
    How much did Sally originally invest?

    Let P = her original investment.

    She earns i = 6\% = 0.06 annual interest for n = 5 years.

    At the end of five years, she will have:. P(1.06)^5 dollars.


    She invests this amount at. \frac{7.2\%}{4} = 1.8\% = 0.018 quarterly for 24 quarters.

    At the end of the six years, she will have:. P(1.06)^5\cdot(1.018)^{24} dollars,
    . . which, we are told, will equal \$14,\!784.56.

    There is our equation!. . . . . P(1.06)^5(1.018)^{24} \;=\;14,\!784.56


    \text{Solve for }P\!:\;\;P \;=\;\frac{14,784.56}{(1.06)^5(1.018)^{24})} \;=\; 7199.9989497


    Therefore, Sally originally invested \$7,\!200.
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  3. #3
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    Re: Compound interest : Present value

    ohh okay thank you I get it now
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  4. #4
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    Re: Compound interest : Present value

    And how do we do this :
    Tia is investing $2500 that she would like to grow to $6000 in 10 years. At what annual interest rate, compounded quarterly, must Tia invest her money?
    So i know that A=$6000 and Present value= $2500 and n=40 but how do i get the interest rate ?
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  5. #5
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    Re: Compound interest : Present value

    Hi,
    As Soroban points out, A=P(1+i/4)^n, where i is the annual interest rate and n = 40.
    So you need to solve 6000=2500(1+i/4)^{40} for i.

    Compound interest : Present value-mhfinterest.png
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