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Thread: Math Questions

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    Math Questions

    I am stuck on a couple math questions, from my practice test for the final so I'll post them on here and see if you guys can figure out how to set them up. I have the answers because it shows just the answer once you miss it but it doesn't show how to do it.

    1. An individual retiremant account (ira) has $16,000 in it, the owner decides not to add any more money to the account other than interest earned at 7% compounded daily. How much will be in the account 31 years from now when the owner reaches retirement age?

    The answer is 140,103.39

    2. How many 8-letter code words are possible from the first 12 letters of the alphabet if no letter is repeated? If the letters can be repeated? If adjacent letters must be different?

    A. if no letter is repeated- 19,958,400
    B. If letters can be repeated- 429,981,696
    C. If adjacent letters must be different- 233,846,052

    Thanks to anyone who understands how to set these problems up!



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    Re: Math Questions

    2a) 12*11*10*9*8*7*6*5...you have 12 letters to pick from, then 11, then 10, etc.
    b) 12^8...you can pick from all 12 in any spot
    c) 12*11*11*11*11*11*11*11...you can pick from any of the numbers at first, but you can't select that number again, so you have 11 to pick from.



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    Re: Math Questions

    Quote Originally Posted by lennon3 View Post
    I am stuck on a couple math questions, from my practice test for the final so I'll post them on here and see if you guys can figure out how to set them up. I have the answers because it shows just the answer once you miss it but it doesn't show how to do it.

    1. An individual retiremant account (ira) has $16,000 in it, the owner decides not to add any more money to the account other than interest earned at 7% compounded daily. How much will be in the account 31 years from now when the owner reaches retirement age?

    The answer is 140,103.39

    2. How many 8-letter code words are possible from the first 12 letters of the alphabet if no letter is repeated? If the letters can be repeated? If adjacent letters must be different?

    A. if no letter is repeated- 19,958,400
    B. If letters can be repeated- 429,981,696
    C. If adjacent letters must be different- 233,846,052

    Thanks to anyone who understands how to set these problems up!
    Okay, I can help you on number 2.

    A. if no letters are repeated, for your first letter you have 12 options, for you next letter you have 11, then for the 3rd letter 10 options.... so you are looking at 12x11x10x9x8x7x6x5=19,958,400.

    B. if letters can be repeated, then you have 12 options for each letter. 12x12x12x12x12x12x12x12=429,981,696.

    C if adjacent letters must be different, then you have 12 choices for the first letter, then 11 for the letters after that.
    12x11x11x11x11x11x11x11=233,846,052



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    Re: Math Questions

    Try this for number 1

    M = P( 1 + i )^n ---- this is the quantity 1+i taken to the n'th power... not sure how to type the exponent.

    M is the final amount including the principal.

    P is the principal amount.

    i is the rate of interest per time period.

    n is the number of time periods invested.

    You didn't mention it in the problem, but I would guess that 7% is an annual rate, so you would need to convert it to a daily rate if that is the case. And then n would be the number of days you are invested and P would be the initial 16k.



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    Re: Math Questions

    Quote Originally Posted by lennon3 View Post
    I am stuck on a couple math questions, from my practice test for the final so I'll post them on here and see if you guys can figure out how to set them up. I have the answers because it shows just the answer once you miss it but it doesn't show how to do it.

    1. An individual retiremant account (ira) has $16,000 in it, the owner decides not to add any more money to the account other than interest earned at 7% compounded daily. How much will be in the account 31 years from now when the owner reaches retirement age?

    The answer is 140,103.39

    2. How many 8-letter code words are possible from the first 12 letters of the alphabet if no letter is repeated? If the letters can be repeated? If adjacent letters must be different?

    A. if no letter is repeated- 19,958,400
    B. If letters can be repeated- 429,981,696
    C. If adjacent letters must be different- 233,846,052

    Thanks to anyone who understands how to set these problems up!
    1. A = future amount
    P = current principal = 16,000
    r = annual compunding rate = 0.07
    N = number of times compounded/year = 365
    t = number of years = 31

    A = P((1+ (r/N))^(Nt))

    2. A) number of permutations of 8 letters from a set of 12. = 12!/(12 - 8)!
    B) 12^8
    C)12* (11^7) : 12 choices for first letter, 11 for each of the last 7.


    Last edited by dornstar44; 12-15-2010 at 07:06 PM.

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    Re: Math Questions

    Quote Originally Posted by dornstar44 View Post
    1. A = future amount
    P = current principal = 16,000
    r = annual compunding rate = 0.07
    N = number of times compounded/year = 365
    t = number of years = 31

    A = P((1+ (r/N))^(Nt))
    This. 16,000 * (1+.07/365)^(31*365) = 140,103.39



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    Re: Math Questions

    Quote Originally Posted by IcSyU View Post
    This. 16,000 * (1+.07/365)^(31*365) = 140,103.39
    Alright thanks a lot guys, you helped a lot... I understand the second question completely and should be able to get the first one after I read over what you guys said again lol.



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    Re: Math Questions

    Quote Originally Posted by lennon3 View Post
    Alright thanks a lot guys, you helped a lot... I understand the second question completely and should be able to get the first one after I read over what you guys said again lol.

    For the first one, just make sure everything is using the same time period. Since the interest compounds daily, you need to convert the 31 years to days (365*31) and divide the APR by 365. Once everything's in the same units, you can just use F=P(1+i)^n. I think of it as future value=present value (1+i)^n, if you want to find the present value of a future return, use the same equation, but to the (-n) power



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    Re: Math Questions

    for #1 don't forget about leap years



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    Re: Math Questions

    Quote Originally Posted by cs6804 View Post
    for #1 don't forget about leap years
    For leap years, the daily rate changes to offset the extra day, because the 7% annual rate is constant whether it's a leap year or not. Making this assumption may not be exact, but it's going to be a pretty doggone close approximation (well beyond any significant figures the professor could want).



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    Re: Math Questions

    Quote Originally Posted by dornstar44 View Post
    For leap years, the daily rate changes to offset the extra day, because the 7% annual rate is constant whether it's a leap year or not. Making this assumption may not be exact, but it's going to be a pretty doggone close approximation (well beyond any significant figures the professor could want).
    In all my works with economics (engineering economics), 1 year= 365 days (even on the FE). I would use this on your exam, but if you feel your prof might question you on it, just write down this assumption. However, you should be fine.



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