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Cigarretes are expensive!(compound interest problem)

  1. Aug 10, 2006 #1
    I've been circling his problem for a little while and cannot find how to approach it.

    A typical smoker spends 55 dollars a month on cigarrettes. Suppose that the smokers invest at the end of the month that same amount in a savings account at 4.8% compounded monthly. How much money will be in the account at the end of 40 years?


    I translated that from spanish so it might be a little unclear, polease dont hesitate to ask for clarifycation.

    I know that the compound interest formula is A= P(1+(r/n)^nt but the problem is that everytime I make a deposit I have to add last month amount with interest plus this months amount and it keeps mounting every month. I think the problem lies in P. I Tried plugging in all the numbers and if I invest only the first 55 dollars I will have 2305.60 at the end of the 40 years but I know thats wrong, as the real amount should be much higher. Any push in the right direction would me appreciated greatly. Thanks
     
  2. jcsd
  3. Aug 10, 2006 #2
    I just scratched this out on paper, and im trying to get a general solution for this: F = [1+(i/n)^nt]*A + [1+(i/n)^nt-1]*A + [1+(i/n)^nt-2]*A + ...
    so its like calculating n different accounts, each with the same principle investment, just with one less compounding term for each successive account
     
  4. Aug 10, 2006 #3
    Shouldn't A change over time too?

    btw thanks for the reply
     
  5. Aug 10, 2006 #4
  6. Aug 10, 2006 #5
    Thanks for the link Ronnin it really helped a lot.

    I found a different formula in here
    mathforum.org

    but they both gave me the same result.
    The website you gave me used (a - ar^(n+1))/(1-r) where;

    a=deposit (55)
    r=the rate (1+(.048\12))
    n=479 (from the geometric sequence?)

    I then substituted and

    (55-55(1.004)^480)\(-.004)=79679.7


    The other formula P = M([1+(i/q)]^nq-1)(q/i) where;

    M= 55
    i= .048
    q=12
    n=40

    gave me the same result.

    My only confusion is that I tried to verify with a web calculator here, but it gave a number that it is a bit higher, can someone verify for me? Thanks again
     
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