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Math Help - interest savings

  1. #1
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    interest savings

    The answer to the following question is $13,791.60. I would like to know what formulas to use and in what order to arrive at this answer. thanks.



    A person purchased a $131,637 home 10 years ago by paying 15% down and signing a 30 year mortgage at 9% compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 30 year mortgage at 5.4% compounded monthly. How much interest will refinancing save? (round to the nearest cent as needed)
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  2. #2
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    This is a long problem for us to do, even just giving you a list of formulae to apply. Post your attempt.

    1) Find the premium on the original loan

    2) find the balance outstanding after 10 years

    3)hence find the total interest payable in the final 20 years

    4) find the premium on the revised loan

    5) hence find the total interest payable on the revised loan.

    6) subtract (5) - (3)
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  3. #3
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    initial mortgage = 131,637.00(0.85) = 111,891.45

    P(1 + .0075)^360

    total cost of initial mortgage: P(1 + .0075)^360 = 1648225.5217423364730002528837901
    total interest to be paid: 1648225.5217423364730002528837901 - 111,891.45 = 1536334.0717423364730002528837901
    3) interest to be paid in last 20 years: 1536334.0717423364730002528837901 / 3(2) = 1024222.7144948909820001685891934
    principal paid in first 10 years: 111,891.45 / 3(2) = 74594.3

    refinance mortgage: 74594.3
    total cost of refinance mortgage: P(1 + .0075)^360 = 375564.41271328714606130866041724
    5) total interest to be paid: 375564.41271328714606130866041724 - 74594.3 = 300970.11271328714606130866041724

    300970.11271328714606130866041724 - 1024222.7144948909820001685891934 = a negative number and not $13,791.60. Where am I going wrong?
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  4. #4
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    I cant follow your working. Key steps (eg, the calculation of P) dont appear to be shown.

    Here are the calculations for the original loan: I assume premiums are paid in arrear and i have not used the 2dp rounding specified in the question, so your figures will differ slightly.

    Monthly interest rate: i = 0.09/12 = 0.0075
    v=1/(1+i)

    Initial balance: 111891.45
    Term: 360 months

    Monthly premium:
    P \frac{1-v^{360}}{i} = 111891.45

    124.2818657P = 111891.45

    P = 900.30

    Capital outstanding after 10 years
    =Accumulated initial balance - Accumulated premium

    111891.45 \times (1.0075^{120}) - 900.3 \times \left( \frac{(1+i)^{120} - 1}{i} \right)

    274285.9 - 174224.7 = 100064.24

    Capital repaid @10y= 111891.45 - 100064.24 = 11827.21

    Total premiums paid @10y = 120 * 900.3 = 108036.47
    Total interest paid @10y = 108036.47 - 11827.21 = 96209.26

    Total premiums paid @30y = 360 * 900.3 = 324109.41
    Total capital paid @ 30y = 111891.45
    Total interest paid @30y = 324109.41 - 111891.45 = 212217.96

    Total interest payable between 10y and 30y = 212217.96 - 96209.26 = 116008.7


    Now do the calculations on the other loan.
    -Start by finding the premium payable
    -Hence find the total premium paid over the loan
    -hence work out the total interest repaid over the loan (=total premium - initial loan amount)
    -compare this to 116008.7



    Spoiler:

    For the very final answer (interest saved) i got a 13792
    Last edited by SpringFan25; April 12th 2011 at 02:15 AM.
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  5. #5
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    I agree with most of your calculations, SpringFan, bot not your finall answer 0f $13,792 as interest saved.

    I make that $52,226
    And it is this simple to calculate:
    Monthly payment 1st 10 years: 900.30
    Monthly payment last 20 years:682.69

    Interest saved = 240(900.30 - 682.69) = ~$52,226

    Seems to me I posted this 2 days ago...post disappeared...
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