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Math Help - Saving money paying off a home loan in under 10 years

  1. #1
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    Saving money paying off a home loan in under 10 years

    Hi guys, this is my first post so, nice to meet everyone.

    ok, the question goes :

    One of the local financial advisers says that if you are paying off a house you should try to tailer your house repayments so that the loan is paid off as soon as possible but there is little to be saved by paying it off in less than 10 years. Investigate the truth or otherwise of this statement and determine whether there is a mathematical link between time of pay off the loan and savings made.



    I just have no idea on how to tackle this problem, but I'm pretty sure that its something quite small that I'm missing and which is the key to the whole thing. The thing is most confusing because logic tells me that the longer you drag out a loan, the more interest you have to pay, thus the less you pay. My only idea as of right now is to graph the percentage rise in interest paid from one year to another and then hopefully the graph will show a fairly straight line in the amount of interest paid for the first 10 years and then start rising to a steeper gradient after that or something. But even if that were the case I'm not sure on how to find the rise in interest paid. Any help will be appreciated, cheers
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  2. #2
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    Hello, iced_maggot!

    Welcome aboard . . . hope you like it here.

    If no one is responding, it's that the question is strange . . .


    One of the local financial advisers says that if you are paying off a house, you should
    try to tailor your house repayments so that the loan is paid off as soon as possible.

    But there is little to be saved by paying it off in less than 10 years. .Really?

    Investigate the truth or otherwise of this statement and determine whether
    there is a mathematical link between time to pay off the loan and savings made.
    . . Well, of course there is!
    To minimize the total interest paid, pay cash. .Interest: $0

    . . Otherwise, the longer the mortgage, the more interest you will pay.


    So what exactly are they asking?

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  3. #3
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    yeah i know it really is a strange question. well theyre asking if the financial adviser has any sort of thruth in his comments and im just going on a hunch here but my guess is that he doesnt.

    so i think the best way to do this would be just work out the savings made for each year and say that the less time you take to pay it off, the more you save and that the adviser is smoking drugs.

    also im guessing that this is a trick question as it was menant to be one of the complex questions which would propably explain the strangeness of it all
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  4. #4
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    True, that minimizing interest is not a reasonable goal, but the claim can be investigated. Just make a list of terms and total interest. I'll use 8% Annual Interest, Monthly Payments, and a $100,000 loan.

    30 years - Total Interest $164,155
    25 years - Total Interest $131,544 - Saved $32,611 from previous
    20 years - Total Interest $100,745 - Saved $30,799 from previous
    15 years - Total Interest $72,017 - Saved $28,728 from previous
    10 years - Total Interest $45,593 - Saved $26,424 from previous
    5 years - Total Interest $21,658 - Saved $23,935 from previous

    I think the advisor's point may be: "Wouldn't you rather save $32,000 than a mere $24,000?" The marginal interest savings do indeed decrease as you decrease the term, but ONLY because there is much less interest to decrease! For example, it would be very hard to save another $32,000 from the 5-year term, since there is only $22,000 to save!

    1) Getting out of debt is almost always a good idea.
    2) The specific terms of your contract MAY change the rules of interest if you try to pay it off early.
    3) Certain types of securitization of these loans don't get paid at all if it is paid off too early. This may irritate investors and motivate a more sever implementation of point #2.
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  5. #5
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    Thanks TKHunny

    I think that may be what the question is asking. But just in case, i might put in both points just to be sure. Quite abstract thinking tho, good work and thanks.

    and also just one more thing, what do you think it could mean when it says mathematical link between the time to pay off the loan and savings made? is there some sort of function or formula that i'm not aware of or is it more of a "yes there is" sort of thing?
    Last edited by iced_maggot; August 16th 2007 at 08:00 PM.
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  6. #6
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    Quote Originally Posted by TKHunny View Post
    True, that minimizing interest is not a reasonable goal, but the claim can be investigated. Just make a list of terms and total interest. I'll use 8% Annual Interest, Monthly Payments, and a $100,000 loan.

    30 years - Total Interest $164,155
    25 years - Total Interest $131,544 - Saved $32,611 from previous
    20 years - Total Interest $100,745 - Saved $30,799 from previous
    15 years - Total Interest $72,017 - Saved $28,728 from previous
    10 years - Total Interest $45,593 - Saved $26,424 from previous
    5 years - Total Interest $21,658 - Saved $23,935 from previous

    I think the advisor's point may be: "Wouldn't you rather save $32,000 than a mere $24,000?" The marginal interest savings do indeed decrease as you decrease the term, but ONLY because there is much less interest to decrease! For example, it would be very hard to save another $32,000 from the 5-year term, since there is only $22,000 to save!

    1) Getting out of debt is almost always a good idea.
    2) The specific terms of your contract MAY change the rules of interest if you try to pay it off early.
    3) Certain types of securitization of these loans don't get paid at all if it is paid off too early. This may irritate investors and motivate a more sever implementation of point #2.
    I think the question is realy about something like this:

    Case1: you take out a 10 year loan at interest rate r, which has repayments
    p_10 per month. After the 10 years are up you invest p_10 per month at an
    interest rate ri for 15 years.

    Case 2: You take out a 25 year loan at an interest rate r, which has
    repayments p_25 per month (note p_25<p_10 as the interset rates are the
    same), and you invest p_10-p_25 per month at an interest rate ri.

    Thus in both cases you have the same total monthly payments.

    After 25 years which of these cases leaves you with the greater savings?

    RonL
    Last edited by CaptainBlack; August 16th 2007 at 09:22 PM.
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  7. #7
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    Quote Originally Posted by CaptainBlack View Post
    I think the question is realy about something like this:

    Case1: you take out a 10 year loan at interest rate r, which has repayments
    p_10 per month. After the 10 years are up you invest p_10 per month at an
    interest rate ri for 15 years.

    Case 1: You take out a 25 year loan at an interest rate r, which has
    repayments p_25 per month (note p_25<p_10 as the interset rates are the
    same), and you invest p_10-p_25 per month at an interest rate ri.

    After 25 years which of these cases leaves you with the greater savings?

    RonL
    Umm.. huh? how can you invest loan repayments once you've already given them to the lender?
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  8. #8
    Grand Panjandrum
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    Quote Originally Posted by iced_maggot View Post
    Umm.. huh? how can you invest loan repayments once you've already given them to the lender?
    You don't, in one plan the repayments on the loan are less than in the other
    it is the difference that you invest.

    The idea is to compare financial instruments you embed them in composite
    instruments with the same payments then evaluate either the present or
    future values of the composite instruments. In this case a future value 25
    years hence is the natural planning horizon so the FV at that time is what
    is to be compared.

    RonL
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  9. #9
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    oh, rite so its the difference you invest to see which one makes more money

    alrite ill put that case in as well then, cheers
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  10. #10
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    Quote Originally Posted by CaptainBlack View Post
    I think the question is realy about something like this:

    Case1: you take out a 10 year loan at interest rate r, which has repayments
    p_10 per month. After the 10 years are up you invest p_10 per month at an
    interest rate ri for 15 years.

    Case 2: You take out a 25 year loan at an interest rate r, which has
    repayments p_25 per month (note p_25<p_10 as the interset rates are the
    same), and you invest p_10-p_25 per month at an interest rate ri.

    Thus in both cases you have the same total monthly payments.

    After 25 years which of these cases leaves you with the greater savings?

    RonL
    It is not unknown for the tax system to offer breaks for home loan
    repayments or regular savings, and if that is the case these would have to
    be factored into the analysis.

    RonL

    (PS for a long time the UK Government offered tax relief on home loans
    which resulted in the effective interest rate on home loans being less than
    the market risk-free interest rate, so your best plan was to take as long
    a loan as possible for an amount up to the limit which attracted the tax break.
    It also helped that property prices were growing at real rates of 25-50%
    per annum - in the mid 1980's my house was earning more than I was!)
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  11. #11
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    Quote Originally Posted by CaptainBlack View Post
    I think the question is realy about something like this:
    Tough call. There does seem to be a theme, here. We're all wondering what the actual question is.

    Iced:
    I like the reinvestment question. Payments are not made to the lender and then reinvested. In the first case, only 10 years are paid to the lender. The next 15 years are invested. Ponder on the second and see what it is doing.

    In the question I was trying to answer, I made the assumption that you already have locked in some amount of interest to pay and were thinking about reducing the interest paid. It is a different question.

    So, what REALLY is the question? Anyway, there is plenty of stuff to think about that already has been presented.
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  12. #12
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    yeah it was my understanding that i was trying to minimize the amount of interest paid as well, however with problems like these they make it intentionally vague so you don't know exactly what they're asking and you have to take a stab at it (damn australian education system) but anyway, I think i've got all I need for a satisfactory answer, thanks again guys
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  13. #13
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    Re: Saving money paying off a home loan in under 10 years

    Quote Originally Posted by TKHunny View Post
    True, that minimizing interest is not a reasonable goal, but the claim can be investigated. Just make a list of terms and total interest. I'll use 8% Annual Interest, Monthly Payments, and a $100,000 loan.

    30 years - Total Interest $164,155
    25 years - Total Interest $131,544 - Saved $32,611 from previous
    20 years - Total Interest $100,745 - Saved $30,799 from previous
    15 years - Total Interest $72,017 - Saved $28,728 from previous
    10 years - Total Interest $45,593 - Saved $26,424 from previous
    5 years - Total Interest $21,658 - Saved $23,935 from previous

    I think the advisor's point may be: "Wouldn't you rather save $32,000 than a mere $24,000?" The marginal interest savings do indeed decrease as you decrease the term, but ONLY because there is much less interest to decrease! For example, it would be very hard to save another $32,000 from the 5-year term, since there is only $22,000 to save!

    1) Getting out of debt is almost always a good idea.
    2) The specific terms of your contract MAY change the rules of interest if you try to pay it off early.
    3) Certain types of securitization of these loans don't get paid at all if it is paid off too early. This may irritate investors and motivate a more sever implementation of point #2.
    this is correct...i agreed with this...

    www.drugaddiction-recovery.com
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