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Math Help - confused

  1. #1
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    Question confused

    Bob deposited $25k in a savings account @ 10% interest compounded semiannually. At the beginning of year 4 he deposited another $40k @10% compounded semiannually. At the end of 6yrs, what is the balance in his account? I have worked it out several ways, but now I am unsure of which way to go....

    3yrsx2=6 periods
    10% /2=5%

    25000x1.7716 (per table in my book)=44290-25000=$19290 interest for 4yrs off $25000

    2yrsx2=4 periods

    40000x1.4641=58564-40000=18564 interest for 2 yrs off $40000

    25000+40000+19290+18564=102,854

    I also worked it out this way.......

    4yrsx2=8 periods; 5%

    25000x2.1436(book table)=53590-25000=$28590 interest for 4 yrs off $25000

    40000x1.4641=5864-40000=18564 interest for 2yrs off $40000

    25000+40000+28590+18564=$112154
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  2. #2
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    Re: confused

    really? ... does $19290 interest on a 3 year investment of $25000 at 10% make sense?
    if so, let me know where that institution is ... I'll deposit all I have ASAP.

    general equation for compounded interest is

    A = P\left(1 + \frac{r}{n}\right)^{nt}

    where A = account balance after t years paid at an APR of r, compounded n times a year.

    after 3 years ...

    A = 25000(1.05)^6 = 33502.39

    add 40000 at the end of year 3 ...

    A = 73502.39(1.05)^6 = 98500.23 at the end of 6 years
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  3. #3
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    Re: confused

    You could also do this by calculating the balance on the first amount for the full 6 years: 25000(1+ .05)^{12}= (25000)(1.7958)= 44896.41
    the the balance on the second amount for three years: 40000(1.05)^{6}= (40000)(1.3401)= 53603.82 and then adding: $98500.23.

    The powers of "12" and "6" are, of course, the 12 "half years" in 6 years and 6 "half years" in 3 years. And, of course, the "1.05" is the 10% per year divided by 2 since we are dealing with half years, together with the "1" for the original amount.
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  4. #4
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    Re: confused

    Quote Originally Posted by businessmgmt View Post
    At the beginning of year 4 he deposited another $40k @10% compounded semiannually.
    That was probably confusing you.
    It is the SAME as "At the end of year 3".
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