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Math Help - Annuity help

  1. #1
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    Annuity help

    You just taken out a $300 000 home loan over 25 years with a fixed 8.25% interest rate (calculated monthly)
    Calculate the amount of your monthly repayments. Home loan calculations are often based on an Annuities formula.
    Note:
    i = Periodic Interest Rate
    n = Number of Periods
    D = Periodic Deposit
    A = Final amount

    Annuity formula

    A = D * ( ( 1 + i ) ^ n – 1 ) / i )
    D = A * ( i / ( 1 + i ) ^ n – 1 ) )


    D = 300 000 [ ( 0.0825 / 12 ) / ( ( 1 + ( 0.0825 / 12 ) ) ^ ( 25 * 12 ) – 1 )]

    Is this formula right? Or am I just writing it out wrong? I went to a banking website and put in the numbers and got this answer:
    D = $2,369.10 Monthly
    Total payment over 25 years $708,432.94

    Can someone tell me what I did wrong in the formula? And what the formula for calculating the total payment over 25 years would actually be? Wouldn't it just be D * 300 (25 years multiplied by 12 months)?
    Last edited by Xcel; March 15th 2008 at 09:45 PM.
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  2. #2
    Senior Member topher0805's Avatar
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    The compound interest formula is:

    M = P(1+i)^n


    M is the final amount including interest.
    P is the principal.
    i is the interest, in decimal form.
    n is the number of periods.

    In this case, since you are compounding monthly, you need to divide i by 12.

    So, you would have;

    M = 300,000(1+\frac {0.0825}{12})^25

    Plug it in to get:

    M = 356,049



    ::EDIT:: Sorry, didn't read your whole question. I'll post a new reply soon.
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  3. #3
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    Yeah, trying to find out how much i need to deposit each month for 25 years =)
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  4. #4
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    Quote Originally Posted by Xcel View Post
    Yeah, trying to find out how much i need to deposit each month for 25 years =)
    2365.35 is your monthly payment and over the life of your loan, assuming you pay on time, not late, not early, you will end up paying 709,605 for the life of the loan. Go here, it will show you the entire math for a home loan mortgage calculation. Let me know if you have questions.

    Mortgage Payment Calculator

    Enter 8.25 for APR, 300000 for Loan, and 25 for years.

    NOTE: The reason the banking site and my site are different by a few bucks is due to rounding of the interest rate. I don't round my interest rate at all when compounding monthly. Most mortgage companies I know may round, but it's 5 digits or more from what I understand.
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  5. #5
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    Thank you so much for that link!
    The amount of detail in that form is perfect, thank you!
    Last edited by Xcel; March 15th 2008 at 11:36 PM.
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