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  1. MHB Apprentice

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    #1
    Hi new to the forum and would like to improve my level of maths. I am working through a text but need some help with a compound interest question.

    the formula to find compound interest is I = P (1 + R)n1.

    P= principal sum
    R= interest rate
    n= number of periods for which interest is calculated

    John borrows 500 over 2 years from a building society at a rate of 12% per annum compounded
    quarterly. How much interest will Shifty have to pay at the end of the 2-year loan?

    If 500 is loaned for 2 years at a rate of 12% per annum, compounded quarterly, the
    calculations need to be made on a quarterly basis. So the value of n will be 4 (quarters) 2 (years)
    = 8, and the value of r will be 12⁄4 = 3% (per quarter).
    According to the question the answer in book is I = 500(1.03)81 = 133.38.

    Now my issue is when i try to do this with my calculator i get the figure 614.9

    I am not sure what I am doing wrong. There are other practice questions, but I want to be sure I am following the correct stages on the calculator before I attempt these. I am using this calculator model

    Any advice would be much appreciated

  2. MHB Journeyman
    MHB Math Helper

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    #2
    You are misunderstanding the formula, "I = P (1 + R)n1".
    To get 614.9 you must have interpreted it as $ \displaystyle I= P(1+ R)^{n-1}$:
    $ \displaystyle 500(1+ .03)^7= 500(1.03)^7= 500(1.29)= 614.9$

    But it is $ \displaystyle I= P((1+ R)^n- 1)$:
    $ \displaystyle 500((1+ .03)^8- 1)= 500(1.03^8- 1)= 500(1.2667- 1)= 500(0.267)= 133.38$.

    $ \displaystyle P(1+ R)^n$ is the amount, both initial amount and interest, that must be repaid. The -1, which, after multiplying by P is -P subtracts off the initial amount to leave interest only.

  3. MHB Apprentice

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    #3 Thread Author
    Quote Originally Posted by HallsofIvy View Post
    You are misunderstanding the formula, "I = P (1 + R)n1".
    To get 614.9 you must have interpreted it as $ \displaystyle I= P(1+ R)^{n-1}$:
    $ \displaystyle 500(1+ .03)^7= 500(1.03)^7= 500(1.29)= 614.9$

    But it is $ \displaystyle I= P((1+ R)^n- 1)$:
    $ \displaystyle 500((1+ .03)^8- 1)= 500(1.03^8- 1)= 500(1.2667- 1)= 500(0.267)= 133.38$.

    $ \displaystyle P(1+ R)^n$ is the amount, both initial amount and interest, that must be repaid. The -1, which, after multiplying by P is -P subtracts off the initial amount to leave interest only.
    Thank you so muc HallsofIvy for your prompt reply I suspected it was something to do with my use of brackets. Its just something I need to improve on. Apologies for late response and thanks again.

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