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Math Help - Help in calculating interest rate.

  1. #1
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    Help in calculating interest rate.

    Hi to all, I have been reading this site and hope that someone will be able to help with some figures and calculations that I have.

    I have been trying to find the answer for a very long time and really hope that there are some wizards who can crack the answer.

    I want to know if the interest rate has been calculated correctly please.

    I have a loan of 37,672.00 for 303 months.

    The first 3 months I don't have to pay anything.

    Then I have to pay 285.79 for 12 months at an interest rate of 7.80%

    Then I have to pay 335.79 for 288 months at an interest rate of 9.80%

    I have tried doing this myself by 37,672.00 x 7.80% and 9.80% but admit that I am hopeless at getting the figures to match.

    Any help or advice will be very much appreciated and thank you in advance
    Last edited by mr fantastic; July 23rd 2010 at 02:31 PM. Reason: Edited title.
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  2. #2
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    Quote Originally Posted by jewels View Post
    I have tried doing this myself by 37,672.00 x 7.80% and 9.80% but admit that I am hopeless at getting the figures to match.
    So you have never dealt with financial formulas.

    Well, the payments as specified in your problem are correct;
    telling you WHY and HOW is almost impossible, since you don't know the basics.
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  3. #3
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    Wilmer is right, the gap between your method and the right answer is very very big and not easy to bridge here. You could try getting a financial maths text book from your library or reading one of these links

    Calculate Mortgage - How to Calculate Mortgage Payments

    http://www.mathhelpforum.com/math-he...nt-values.html
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  4. #4
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    Quote Originally Posted by SpringFan25 View Post
    Wilmer is right, the gap between your method and the right answer is very very big and not easy to bridge here. You could try getting a financial maths text book from your library or reading one of these links

    Calculate Mortgage - How to Calculate Mortgage Payments

    http://www.mathhelpforum.com/math-he...nt-values.html

    Thank you guys for your comments and i will have a try at the links you have given.

    Wilmer is it possible that you could try and explain how you would do these figures please? if it is too much I understand and thank you all the same.
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  5. #5
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    You did not specify the interest rate that applies in the first 3 months (when you pay no premium). It appears to be 0%.

    So, at the end of the 3 months you still have 37672 to pay off.

    The monthly premium (paid in arrear) for a 300 month loan at a interest rate of 7.8% (convertible monthly) can be found as follows:

    effective monthly rate: 7.8% / 12 = 0.65%

    i=0.0065
    v=1/(1.065) = 0.993542
    n = 300

    PV(premium) = Loan amount

    P \times \frac{1-v^n}{i} = 37672

    131.8193P = 37672

    P = 285.785 \approx 285.79


    That gives you your initial premium, which is paid for 12 months. After 1 year, the new premium will have to pay off the outstanding loan balance in 288 months. The first thing we need to do is find the outstanding loan balance.

    Outstanding Debt = Accumulated Loan - Accumulated premium

    = 37672 * (1.0065^{12}) - 285.79 \frac{(1+i)^{12} - 1}{i}

    =40717.77406 - 285.79 \times 12.43843236

    =40717.7 - 3554.8

    =37163.05

    Now that we have the outstanding loan amount at the end of year 1, we must calculate the premium that needs to be paid to clear the debt in 288 months.

    effective monthly rate: 9.8% / 12 = 0.817%

    For use in calcs:
    i= 0.00816666
    v = 0.991899
    n=288

    PV(prem) = loan amount

    P \frac{1-v^{288}}{i} = 37163.05

    110.6826 * P = 37163.05

    P = 335.76

    (i assume the difference between this and your figure is due to rounding at some point in the intermediate calculations, although its possible i have made a mistake in the method instead)

    In each case, the method used to find the premium is to equate the present value of the premiums to the loan amount.
    Last edited by SpringFan25; July 24th 2010 at 02:52 PM.
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  6. #6
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    Quote Originally Posted by jewels View Post
    I want to know if the interest rate has been calculated correctly please.
    I have a loan of 37,672.00 for 303 months.
    The first 3 months I don't have to pay anything.
    Then I have to pay 285.79 for 12 months at an interest rate of 7.80%
    Then I have to pay 335.79 for 288 months at an interest rate of 9.80%
    You know the rates are correct after these 2 "tests":

    1: If I pay 285.79 per month for 12 months against a loan of 37672 at a rate of 7.8%
    compounded monthly, how much will I owe after the 12th payment?
    Answer: 37163.05
    Calculated this way:
    i = .078/12: 37672(1 + i)^12 - 285.79[(1 + i)^12 - 1] / i = 37163.05

    2: If the rate then goes up to 9.8% compounded monthly, what must I repay monthly
    so that the loan is paid off after 288 payments?
    Answer: 335.79
    Calculated this way:
    i = .098/12: 37163.05i / (1 - 1/(1 + i)^288) = 335.79

    Hope that helps.
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  7. #7
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    Thank you very much wilmer and springfan25, the way you both have broken it down and calculated this for me has really sunk in, and I have understood.

    My loan agreement was a bit hazy and I am so glad I joined on here, as there are some very good people here. My agreement read below, which I think you will agree matches the same figures that you guys made.

    "This is a variable interest rate loan". The Concessionary Interest Rate charged in the first 3 months will be 0.00%. After this period, there will be a Discount of 2.00% off the Annual Nominal Rate for 12 months giving a rate payable of 7.80%. When the Discount period ends, we will charge interest at your Annual Nominal Rate which is currently 9.80% for the remainder of the loan term. This is a Monthly Rate of 0.82%>

    3 monthly payments of 0.00 followed by 12 monthly payments of 285.79, followed by 288 monthly payments of 335.76 (assuming no variation in the rate of interest per month). The first payable 1 month after draw down of the Total Loan Facility then on the same each month or on the last day of any month which does not contain a corresponding date. The number of monthly payments and/or the amount of each month may be varied.
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    sorry but i just wanted to ask have you used compound interest to calculate my figures? because i see that you both worked this matter out correctly and have arrived to the same figures on my agreement.

    Just that I do not know what formula my lender was using to calculate the interest, bank of england tracker etc etc. Looks like they are using compound interest? that is why your figures match accurately.
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  9. #9
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    Quote Originally Posted by jewels View Post
    sorry but i just wanted to ask have you used compound interest to calculate my figures? because i see that you both worked this matter out correctly and have arrived to the same figures on my agreement.

    Just that I do not know what formula my lender was using to calculate the interest, bank of england tracker etc etc. Looks like they are using compound interest? that is why your figures match accurately.
    YES, they are using compound interest, as we did.
    Using .078/12 and .098/12 means monthly compounding.

    In Canada, our "Truth in Lending" act forces us to state (using 7.8% as example):
    7.8% annually, compounded monthly, resulting in effective annual rate of 8.085%.
    Calculated this way: (1 + .078/12)^12 - 1 = 1.0808498... - 1 = .0808498... or 8.085% (rounded).

    Looks like you guys in the Land of the Queen are not quite as "truthful"!
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    ooooooooh dear wilmer I did not know you was not in the U.K, in fact I thought this forum was in the U.K. I apologise if I misunderstood. But now that you have given me so much info and help you seem to also have opened up a can of worms.

    Am I correct in saying that my contract is an American contract and if it is so is it allowed to be used in the U.K. There is a term in my loan agreement which reads this agreement will be goverened by English Law that is why I am a bit confused now, as it is a mix of both U.K and U.S.A.

    I do not know what to think or say to that, I did have a feeling judging by the language and terms and conditions in my loan agreemnt that something was not as it should be. I am very grateful and appreciate the help and advice you have given so far.
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  11. #11
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    As far as I know, your contract is FULLY legal (by default, r% compounded monthly is OK).
    If you want to pursue further, this is not the place: see your lawyer.
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  12. #12
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    If this is a real situation rather than an interesting maths problem, you should not be relying anything we say (anything i say anyway, read my signiture).

    If you dont understand a loan product you are being sold, I would think about getting financial advice from a qualified professional.

    You could also check that your lender has a current license:
    Dealing with loan sharks : Directgov - Money, tax and benefits
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  13. #13
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    I think that would be a very good idea to see a lawyer, thank you both for your sound advice and helping me understand the way that the figures have added up.
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  14. #14
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    Quote Originally Posted by SpringFan25 View Post
    If this is a real situation rather than an interesting maths problem, you should not be relying anything we say (anything i say anyway, read my signiture).

    If you dont understand a loan product you are being sold, I would think about getting financial advice from a qualified professional.

    You could also check that your lender has a current license:
    Dealing with loan sharks : Directgov - Money, tax and benefits
    Thank you for that link spring, it is very useful and appreciated very much.

    thanks again
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