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Math Help - savings, interest, inflation etc...

  1. #1
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    savings, interest, inflation etc...

    Hi

    this is the parameters i want to use:


    Initial investment (a)

    deposit per f1 (d) for example 1000 per month

    frequency of deposit per year (f1), f1=12 if it is per month

    frequency of compound (f2)

    interest or growth per year (g)

    inflation(i)

    years (n)

    I would like to find the formula where you can answer the question:

    you start with a one time initial investment (i) of 5000$ and then you add 1000$ (d) per month (f) for 8 years (n).

    the growth or interest is 7% (g) per year (f2) and the inflation 3%.


    the calculations are similar to this one, but also includes initial investment.

    interest - Wolfram|Alpha



    I've come up with an easier version, not including initial investment or f2 (it only works for annual compounding of g).

    It looks like this:

    (d(1+((g-i)/f)^(fn)-1)/((g-i)/f)


    this one is a bit simplified though. I dont know how to do it. ive been looking around for instance here:
    Time value of money - Wikipedia, the free encyclopedia
    but have not yet found the correct formula. Please help

    /TT
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  2. #2
    MHF Contributor
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    Ottawa, Canada
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    Quote Originally Posted by Lobotomy View Post
    (d(1+((g-i)/f)^(fn)-1)/((g-i)/f)
    You need to convert the interest rate such that when compounded at a
    frequency equal to the payments frequency, the result is the same as
    the "quoted rate frequency"...quite a mouthful, I know!
    EXAMPLE: on a monthly payment loan, if the rate is quoted as 12% compounded
    semiannually, then a rate compounded monthly needs to be calculated in order to
    make it "fit" the formula.

    Using g as the quoted annual rate compounding semiannually and h as the "monthly" rate:
    (1 + h/12)^12 = (1 + g/2)^2 ; do the math to get:
    h = 12[(1 + g/2)^(1/6) - 1]

    With g = 12% : h = 12[(1 + .12/2)^(1/6) - 1] = .1171055... (or 11.71%).

    In other words, charging interest 12 times per year at 11.71% is the same
    as charging interest 2 times per year at 12%.

    With your formula, I suggest you replace (g-i) with k,
    where k = h - i and h = as above.

    Treat the initial investment (call it A) separately:
    A(1 + k/12)^(fn)

    Hope I was clear enough; not too easy to explain without chalkboard
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