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Math Help - Simple and Compound Interest Problem

  1. #1
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    Simple and Compound Interest Problem

    Hi All,


    Q:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

    1. $ 5500
    2. $ 11000
    3. $ 22000
    4. $ 2750
    5. $ 44000
    Answer Explanation...

    1. Interest for the first year of the simple compound bond is 275/2 - $275.
    2. So we need to determine the rate of interest based on this so...

    605 - 550 = 55. That's the difference between the interest earned on the simple vs compound interest bonds.

    55/275 * 100/1 = 11/55 * 100/1 = 20% Interest

    3. 275 represents 20% interest of a number
    275/20 * 100/1 = 55/4 * 100/1 = $1375.

    4. This represents half the money so 1375*2 = $2750. (D).

    My questions is: Why are we using 55. I.E. The difference between the two interest to determine the interest in 2. What does this 55 represent (besides the difference between the two?)

    Thanks in Advance.
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  2. #2
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    Hello, dumluck!

    I'm not impressed with their explanation.


    Q: Shawn invested one half of his savings in a bond
    that paid simple interest for 2 years and received $550 as interest.
    He invested the remaining in a bond that paid compound interest, compounded annually,
    for the same 2 years at the same rate of interest and received $605 as interest.

    What was the value of his total savings before investing in these two bonds?

    . . 1.\;\$5500 \qquad 2.\;\$11000 \qquad 3.\;\$22000 \qquad 4.\;\$2750 \qquad 5.\;\$44000

    Let \,r be the annual interest rate for both accounts.

    Let \,P be the amount invested in each account.


    He invested \,P dollars at \,r percent simple interest for 2 years.
    . . This earned: . P(r)(2) \:=\:2Pr dollars in interest.
    So we have: . 2Pr \:=\:550 \quad\Rightarrow\quad P \:=\:\dfrac{275}{r} .[1]

    He invested \,P dollars at \,r percent compounded annualy for 2 years.
    . . This grew to: . P(1+r)^2 dollars in two years.
    His interest is: . P(1+r)^2 - P \;=\;P\left[(1+r)^2 - 1\right] dollars.
    . . So we have: . P(2r + r^2) \:=\:605 .[2]

    Substitute [1] into [2]: . \dfrac{275}{r}(2r + r^2) \:=\:605

    . . . . . . 2 + r \:=\:\dfrac{605}{275}\:=\:2.2 \quad\Rightarrow\quad r \:=\:0.2

    Substitute into [1]: . P \:=\:\dfrac{275}{0.2} \:=\:1375

    Hence, he invested \$1375 in each account.


    Therefore, he invested a total of \$2750.

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  3. #3
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    Quote Originally Posted by dumluck View Post
    My questions is: Why are we using 55. I.E. The difference between the two interest to determine the interest in 2. What does this 55 represent (besides the difference between the two?)
    Code:
    Simple interest:
    0            1375.00
    1   275.00   1650.00
    2   275.00   1925.00
    Compound interest:
    0            1375.00
    1   275.00   1650.00
    2   330.00   1980.00
    The 55 is the interest on the 275 (275 * .20 = 55) paid at end of 1st year
    (in the compound interest case, of course); makes 2nd year interest = 330
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