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Calculate the mortagage he could assume for each amortization period

  1. May 13, 2005 #1
    Bob estimates he can afford a monthly mortgage payment of $575. Current interest rates are 6.75%. Calculate the mortagage hecould assume for each amortization period.
    A) 15 years

    the extra info is that the monthly payments per $1000 for this percentage + 15years is $8.85.

    How would you do this problem? :confused:
     
  2. jcsd
  3. May 13, 2005 #2

    JamesU

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    Gold Member

    Do you wanna cheat
     
  4. May 14, 2005 #3
    What have you done so far?
     
  5. May 14, 2005 #4
    Actually most people who do this possess a financial calculator. The formula is derived at http://www.moneychimp.com/articles/finworks/fmmortgage.htm

    P(z^n)-a((z^n)-1)/(z-1) = debt remaining.

    Here, z=(1+i), where i is interest per payment. a is the payment, P is the principal borrowed, and n is the number of payments made.
     
    Last edited: May 14, 2005
  6. May 16, 2005 #5
    the formula used is A=Ao (1+ i) ^n
    A= amount after
    Ao=amount before ( principle amount)
    i=interest rate
    n=time period
     
  7. May 16, 2005 #6
    How about trying 575/8.5*1000=64972. Otherwise, amount assumed equals present value of future payments where interest interest is compounded monthly.
    Mortgage Amount= 575* Sum[((1+(.0675/12))^(-k)),k=1,2,...,12*15]=
    575* [1-(1+(.0675/12))^(-15*12)]/(.0675/12).
     
  8. May 17, 2005 #7
    answerseeker: the formula used is A=Ao (1+ i) ^n. That is not correct because we regularly subtract the monthly payment from the principal.

    LittleWolf: How about trying 575/8.5*1000=64972. Sounds pretty good. Sum[((1+(.0675/12))^(-k)), As far as that goes, I don't think it does any good to sum.

    My calculator, HP15C, takes it straight across from the formula I put previously. That is for this case:

    [tex]P=\frac{a(z^n-1)}{z^n(z-1)}[/tex]

    Putting in $575 for a, 1.005625 for z, n = 180, since it is a monthly payment. Then, I arrive at $64978.40. REMEMBER: 6% is not 6, it is .06 in decimal form. Thus 6.75%/12 = .005625.
     
    Last edited: May 17, 2005
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