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Math Help - Amortization - payer made an extra payment

  1. #1
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    Amortization - payer made an extra payment

    Dad sold a piece of property on 8/17/2007 and financed $100,000.00 at 8% for 10 years, so the buyer is supposed to make annual payments each August 17 of $14902.95. On 1/22/2008, he made a payment of $50,000.00, and he wants to reduce his annual payment, but keep the 10-year length. How do I calculate the new payments?
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by TedDawson View Post
    Dad sold a piece of property on 8/17/2007 and financed $100,000.00 at 8% for 10 years, so the buyer is supposed to make annual payments each August 17 of $14902.95. On 1/22/2008, he made a payment of $50,000.00, and he wants to reduce his annual payment, but keep the 10-year length. How do I calculate the new payments?
    i think, the time is weird, but this is my idea..

    compute for the accumulated value of $50,000.00 on Aug.17,2008 and re-compute for the new payment until the next 9 years after subtracting the accumulated value from $100,000..

    or you can also compute for the present value equal to $100,000 of the sum of $50,000 paid on 1/22/2008 and every R's paid on the 17,Aug. until the 10th year, and solve for R..

    P.S. i really wanted to solve it myself, but it is too late here.. have to sleep..
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  3. #3
    GAMMA Mathematics
    colby2152's Avatar
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    Quote Originally Posted by TedDawson View Post
    Dad sold a piece of property on 8/17/2007 and financed $100,000.00 at 8% for 10 years, so the buyer is supposed to make annual payments each August 17 of $14902.95. On 1/22/2008, he made a payment of $50,000.00, and he wants to reduce his annual payment, but keep the 10-year length. How do I calculate the new payments?
    Find the present value at 8% interest of that January 22nd payment. Subtract that from your $100,000.00 loan. Let's leave that up to you and call it A'.

    A'=\sum_{k=1}^{10} 1.08^{-k}*P

    Solve for P, the newly reduced annual payment.

    *I assumed end of year payments here. To solve for beginning of year payments, you need to subtract $14092.95 from the original loan amount in addition to the present value of $50,000. The next step is to change the limits of the series from (1 to 10) to (1 to 9) because we already subtracted one payment.
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  4. #4
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    Thanks to you both.... I left my notes at the office, but here's what I did:
    1) Divide 8% by 365 to get the daily rate
    2) Multiply the daily rate by the number of days from Aug 17 to Jan 22 to get the finance chg
    3) Added the finance chg to the original balance
    4) Subtract the $50,000 from the new balance
    5) Figure a new amortization schedule with a fresh 10 year term from the January date.

    Everybody involved thought it was fine, so I'm happy, too!
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