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Math Help - Rate of Return

  1. #1
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    Rate of Return

    Can someone help me with this problem?

    "at the end of each yr for the next 10 yrs you will receive $50. Initial investment is $320. what is the rate of return expected?"

    I started by by looking at it this way

    320 = 50 * (1-(1/(1+r)^10))/r

    but impossible to solve...

    p.s. i'm not allowed to use a financial calculator

    do i just estimate it ..that will take forever and i'm not sure if there will be tables on the exam

    Any suggestions?
    Thanks.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by reneebu View Post
    Can someone help me with this problem?

    "at the end of each yr for the next 10 yrs you will receive $50. Initial investment is $320. what is the rate of return expected?"

    I started by by looking at it this way

    320 = 50 * (1-(1/(1+r)^10))/r

    but impossible to solve...

    p.s. i'm not allowed to use a financial calculator

    do i just estimate it ..that will take forever and i'm not sure if there will be tables on the exam

    Any suggestions?
    Thanks.
    If at the end of each year you will receive only $50, then the investment is in simple interest only. It is not compounding.
    A = P + r*P*t
    A = P +(r*P)t
    A = P(1 +rt)
    where
    A = final amount after t years.
    P = principal or initial amount.
    r = interest rate per annum, or yearly rate of return.
    t = time in years

    The "r*P" in your question is $50.
    So,
    r*P = 50
    r(320) = 50
    r = 50/320 = 0.15625
    r = 15.625 percent per annum ---------------answer.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by reneebu View Post
    Can someone help me with this problem?

    "at the end of each yr for the next 10 yrs you will receive $50. Initial investment is $320. what is the rate of return expected?"

    I started by by looking at it this way

    320 = 50 * (1-(1/(1+r)^10))/r

    but impossible to solve...

    p.s. i'm not allowed to use a financial calculator

    do i just estimate it ..that will take forever and i'm not sure if there will be tables on the exam

    Any suggestions?
    Thanks.
    What you have looks OK to me.

    The trial and error should find the answer (approximatly fairly quickly)

    We know the interest rate is less than 50/320 ~= 0.156, so for a first
    guess take r=0.1, and plug it into:

    A=50 * (1-(1/(1+r)^10))/r

    to get A=307.2, so we are on the right track.

    We also try r=0.11, and get A=294.5, so we are going the wrong way.

    So now try r=0.09, and we get A=320.88, which is close.

    (as an alternative to what is described below, at this point you could draw
    a graph of A against r using these three points and estimate the r that
    will give A=320 from that)

    At this point we can accept r=0.09, or do a little linear interpolation
    (or guess the next correction). Changing r from 0.1 to 0.09 chenges A
    from ~307 to ~320, or a change or ~13, we want less change (about 1/15th
    of this change) so we try 0.09 + 0.01/15=0.09067, which gives A=319.9.

    So we find the intrest rate ~0.0907, or 9.1% after rounding to the nearest
    tenth of a percent.

    RonL
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