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xcorect

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  • Apr 17, 2007
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    Kauda danne wal poli hadana suthraya

    කවුද දන්නේ වැල් පොලී හදන සූතය
     

    harshafx

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    Nov 8, 2007
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    Hikzzz...umbath sakvithi wage gemak dennada yanne :lol:
    suthraya nam mathaka na kollo..eth wenne poliyatath poliya hadena ekane. gaana poddak aragena eh widiyata trykarala balapan ethakota suthraya mathaka wei ;)
     

    Airtel

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    Sep 9, 2008
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    In Sri Lanka soon...
    Mathematics of interest rates


    [edit] Simplified Calculation

    Formulae are presented in greater detail at time value of money.
    In the formulae below, i or r are the interest rate, expressed as a true percentage (i.e. 10% = 10/100 = 0.10). FV and PV represent the future and present value of a sum. n represents the number of periods.
    These are the most basic formulae:
    e0ca87a82c591a0e0610792963751fd5.png
    The above calculates the future value of FV of an investment's present value of PV accruing at a fixed interest rate of i for n periods.
    4b5b30b41d1b085e20fc5a5a3825e936.png
    The above calculates what present value of PV would be needed to produce a certain future value of FV if interest of i accrues for n periods.
    36b79c738b8ba926854c017a0544c239.png
    or
    012f25957f86a752650507e4b04fdda1.png
    The above two formulae are the same and calculate the compound interest rate achieved if an initial investment of PV returns a value of FV after n accrual periods.
    8fd9a90e0a838d6af25128576643ba62.png
    The above formula calculates the number of periods required to get FV given the PV and the interest rate i. The log function can be in any base, e.g. natural log (ln)

    [edit] Compound

    Formula for calculating compound interest:
    3c61f664e4b9ae0ea85f89dff6b52548.png

    Where,
    • P = principal amount (initial investment)
    • r = annual nominal interest rate (as a decimal)
    • n = number of times the interest is compounded per year
    • t = number of years
    • A = amount after time t
    Example usage: An amount of $1,500.00 is deposited in a bank paying an annual interest rate of 4.3%, compounded quarterly. Find the balance after 6 years.
    A. Using the formula above, with P = 1500, r = 4.3/100 = 0.043, n = 4, and t = 6:
    a3d51ac5f6c04328671922571dc543d2.png

    So, the balance after 6 years is approximately $1,938.84.

    [edit] Translating different compounding periods

    Each time unpaid interest is compounded and added to the principal, the resulting principal is grossed up to equal P(1+i%).
    A) You are told the interest rate is 8% per year, compounded quarterly. What is the equivalent effective annual rate?
    The 8% is a nominal rate. It implies an effective quarterly interest rate of 8%/4 = 2%. Start with $100. At the end of one year it will have accumulated to:
    $100 (1+ .02) (1+ .02) (1+ .02) (1+ .02) = $108.24
    We know that $100 invested at 8.24% will give you $108.24 at year end. So the equivalent rate is 8.24%. Using a financial calculator or a tableis simpler still. Using the Future Value of a currency function, input
    • PV = 100
    • n = 4
    • i = .02
    • solve for FV = 108.24
    B) You know the equivalent annual interest rate is 4%, but it will be compounded quarterly. You need to find the interest rate that will be applied each quarter.

    0b2d31c8885f746410c62c5106554faf.png
    $100 (1+ .009853) (1+ .009853) (1+ .009853) (1+ .009853) = $104
    The mathematics to find the 0.9853% is discussed at Time value of money, but using a financial calculator or table is easier. Input
    • PV = 100
    • n = 4
    • FV = 104
    • solve for interest = 0.9853%
    C) You sold your house for a 60% profit. What was the annual return? You owned the house for 4 years, paid $100,000 originally, and sold it for $160,000.
    $100,000 (1+ .1247) (1+ .1247) (1+ .1247) (1+ .1247) = $160,000
    Find the 12.47% annual rate the same way as B.) above, using a financial calculator or table. Input
    • PV = 100,000
    • n = 4
    • FV = 160,000
    • solve for interest = 12.47%
    [edit] Example question:

    In January 1970 the S&P 500 index stood at 92.06 and in January 2006 the index stood at 1248.29. What has been the annual rate of return achieved? (ignoring dividends).
    9d0f85bedc9191014f8b03f59998332b.png
    45961ffa8fb9c3c07c35166975e220f3.png
    42e7504ea01258341a9271abfdb6d3c7.png

    [edit] Answer:

    f93a1686770c91a12c07afce83839094.png

    [edit] Doubling

    The number of time periods it takes for an investment to double in value is
    9a67f278e3a45d9793475c572c071784.png
    where
    3714878e9e07938379ca367c604d2b04.png
    is the interest rate as a fraction.
    Let p be the interest rate as a percentage ( i.e., 100 i ). Then the product of p and the doubling time t is fairly constant:
    interest doubling time product

    [edit] Periodic compounding

    The amount function for compound interest is an exponential function in terms of time.
    098237749fc74c8599ba82d9fb3d4b50.png
    • t = Total time in years
    • n = Number of compounding periods per year (note that the total number of compounding periods is
      2d81da8f4c1baf35e1ffce8a5d2a9970.png
      )
    As n increases, the rate approaches an upper limit of er. This rate is called continuous compounding, see below.
    Since the principal A(0) is simply a coefficient, it is often dropped for simplicity, and the resulting accumulation function is used in interest theory instead. Accumulation functions for simple and compound interest are listed below:
    988022ad48425e5532a6ca5ed8350536.png
    79692aac6f7d2bb15b2dee9d9fde32a5.png
    Note: A(t) is the amount function and a(t) is the accumulation function.
     

    xcorect

    Well-known member
  • Apr 17, 2007
    7,881
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    m doo said:
    Minissunta gini gedi denda neda set wenne? :confused: :confused:

    Pissuda heenenwath ehema hithanne na

    oyage sigiyanam cha wage :P

    hena loku file ekakne

    sigiya open wenna patta welawak yanawa

    oka aththatama sigi yakda :P
     

    m doo

    Member
    Jul 16, 2007
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    xcorect said:
    Pissuda heenenwath ehema hithanne na

    oyage sigiyanam cha wage :P

    hena loku file ekakne

    sigiya open wenna patta welawak yanawa

    oka aththatama sigi yakda :P

    Its ok dude.... but oyage ekanam maxxa... patta graphics... matath ekak hadala denda berida brother? lol
     

    m doo

    Member
    Jul 16, 2007
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    xcorect said:
    Mokakda mata molawan kiyanne :confused:

    ok ok now i understood... use spectacles.... its mita molawagena... not mata molawagena.... that means atha mita molawanawa kiyanne...