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Math Help - Compouned mortgage question (can't get the right answer)

  1. #1
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    Compouned mortgage question (can't get the right answer)

    OK the question is "The Samuels have a mortgage of $123000 amortized over 25 years at 7.25% compunded monthly. After the original 4 year term, the mortgage is renewed at 6.5% compunded monthly. Calculate the new monthly payment."

    The answer is $836.90, But I can't get that answer. This is what I did:


    [123000*(0.0725/12)] / [1-(1+(.0725/12))^-300)
    =$889.05 (thats the monthly payment for the 4 years, I need to extract the Principal now)

    P= 889.05- (123000*(0.0725/12)
    =889.05-743.13
    =$145.92 (this is the ammount of principal payed each month, multiply that for 4 years monthly (12*4=48 ))

    $145.92*48= $7004.16 (now subtract from 123000)
    123000-7004.16 = 115995.84

    Now that that is done...THE NEW PAYMENT! (which i can't get correct )

    115995.84*(0.065/12) / [1-(1+(0.065/12))^-252
    and that = $844.87 but the answer is $836.90


    Does anyone know this math and can help me? I don't know where I went wrong. I followed the steps :S...
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  2. #2
    Senior Member
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    Berkeley, Illinois
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    First, we need to calculate the outstanding balance at time 48, which is after the end of 4 years with monthly payments.

    Go here: Principal and Interest Paid Home Loan Amortization Table

    Enter your information. Your selected time is 48. That's the time we want to calculate the outstanding balance immediately after our payment.

    Scroll down through the rows of amortization table. It starts at "Now show the math work for the principal paid, interest paid, and balance at time = 48". After that, it will show you how to calculate the outstanding balance.

    You should get 114901.93.

    Now we need the new monthly payment at 6.5% for 21 more years.

    Go here: Mortgage Payment Calculator

    Enter your info, and I match your answer to the penny.
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  3. #3
    MHF Contributor
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    Quote Originally Posted by Nocholas View Post
    P= 889.05- (123000*(0.0725/12)
    =889.05-743.13
    =$145.92 (this is the ammount of principal payed each month, multiply that for 4 years monthly (12*4=48 ))
    Where did you get that idea? The principal amount changes each month.

    Original Terms

    Rate = 0.0725/12
    Term = 25*12
    PV = $123,000
    Calculate Pmt: $889.05

    After Four Years

    Rate = 0.0725/12
    Term = 21*12
    Pmt: $889.05
    Calculate PV = $114,902.25

    Change Rate

    Rate = 0.065/12
    Term = 21*12
    PV = $114,902.25
    Calculate Pmt: $836.91
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