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Math Help - Mortgage : Yield to Maturity

  1. #1
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    Mortgage : Yield to Maturity

    I have a fixed rate mortgage whose :
    Principal is 150,000
    Maturity is in 2 years
    Interest is compounded monthly at 7%p.a.

    What is the yield to maturity?

    I keep getting 7% for this answer, is this right?

    Thank you in advance
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  2. #2
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    Did you get exactly 7%?

    without (significant) calculation I would expect 7.22%. Can you see why?

    Spoiler:

    if the monthly nominal rate is 7%, the annual effective rate is 7.22%

    PS: i did check this on some sample cashflows to be sure. I assume the first repayment is made in 1 month, and there are 24 repayments total. My calculated premium was 6715.89 per month
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  3. #3
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    Hi there !

    I have a question, as I'm not used to the associated English vocabulary...
    I thought "p.a." means "per annuum" = "per year" ? So why are we talking about a monthly rate ?

    And another question : what exactly do you call a premium here ?

    Are the annuities supposed to be constant ?
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    I have a question, as I'm not used to the associated English vocabulary...
    I thought "p.a." means "per annuum" = "per year" ? So why are we talking about a monthly rate ?
    using international actuariaal notation, which i know you know now

    "7% compounded monthly" normally means

    But if this particular course instructor means i=7%, then the yield to maturity would indeed be 7%.
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    Quote Originally Posted by SpringFan25 View Post
    using international actuariaal notation, which i know you know now

    "7% compounded monthly" normally means i^{12} = 0.07"
    Yep, I understand it this way too, but then why the "p.a." ?
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    i think its just the way they decided to say it 100 years or so ago; probably for marketing reasons ("7% per annum compounded monthly" sounds like more than "0.58% monthly" for savings, and it sounds like less than "7.22% annual" for selling loans)
    Last edited by SpringFan25; May 1st 2011 at 01:03 PM. Reason: bit more on marketing
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    Right, I think I get it now thanks

    (unfortunately, we're not learning the international actuarial notations )

    And I agree it should be 7% given what you explained about the significance of "compounded monthly at 7% pa" ^^
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  8. #8
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    And another question : what exactly do you call a premium here ?

    Are the annuities supposed to be constant ?
    sorry i didn't see those questions. The premium is the monthly repayment on the loan. I assumed it would be level over the term of the loan.
    Last edited by SpringFan25; May 1st 2011 at 02:05 PM.
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    Hi
    Sorry I wasn't clear about the quote - it's supposed to be 7%p.a. and then compounded monthly 0.07/12

    I was given a list of mortgages like the one above, and kept find YTM that were equal to the contract interest rate.

    Also my instructor mentioned to find YTM from a banks point of view, so would this make any difference?
    Last edited by lindah; May 1st 2011 at 02:56 PM. Reason: I've accidentally deleted part of my post
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    Quote Originally Posted by SpringFan25 View Post
    But if this particular course instructor means i=7%, then the yield to maturity would indeed be 7%.
    May I just confirm (sorry!!) that if it was i=7%p.m. then YTM would be 7%?
    And if it is how I originally quoted, then it is an effective annual interest rate calculation?
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  11. #11
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    May I also add that the instructor said, find the YTM from the banks point of view.
    Would that make a difference?
    it wont. the cashflows from the bank's point of view are the same as from the customers, except they have the opposite sign. Its easy to show that this has no effect on the YTM

    YTM i found was exactly the contract interest rate
    Can we see your calculation?

    The only way i can see this as being correct is if you are intentionally expressing the yield to maturity as an annual rate compounded monthly (which may be fine if thats what you were taught), or you are rounding your results excessively.
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    Book2.xlsx.zip

    Here is my calc in excel:
    The Amortization schedule is in the LHS. On the RHS I am discounting the fixed monthly payment $6,715.89 by the 7% yield and getting a PV of $150,000 (I have not included the initial principal payment in the calculations)

    I actually tried to solve for the YTM using Excel's solver
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  13. #13
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    your YTM is expressed as an annual rate convertable monthly. If that is what you've been taught to do then you'll get credit.

    If you express the yield as an annual rate convertable annually then you'll get 7.22% as i said at the top.
    Last edited by SpringFan25; May 1st 2011 at 04:15 PM.
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  14. #14
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    Quote Originally Posted by lindah View Post
    I have a fixed rate mortgage whose :
    Principal is 150,000
    Maturity is in 2 years
    Interest is compounded monthly at 7%p.a.
    What is the yield to maturity?
    Too "vague"; like, is the S150,000 owing NOW, or WAS the original amount?
    "maturity in 2 years" means will be paid off, or will be renegociated?

    Since we don't know at what rate the monthly payments will be reinvested,
    not much can be done, except (1 + .07/12)^12 = 1.07229..., hence
    ~7.23% (as per SpringFan).
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  15. #15
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    Hi Wilmer,

    I agree it is too vague, but that was all I was given!!!
    The $150,000 is the amount now, but we were told to ignore the initial cashflow(so the payout/receipt of the $150,000 principal at t=0 depending whose point of view you take).

    No re-negotiation, and there is no mention of monthly payments being reinvested.

    The question then leads on to calculating duration and convexity of the mortgage I just quoted.
    Its not a very clear question in my opinion.

    Thanks for your thoughts and confirmation of the effective annual interest rate as a YTM
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