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Effective Annual Interest Rate

  1. #1
    John
    Guest

    Effective Annual Interest Rate

    I'm trying to work out the effective annual interest rate for:

    an item can be purchased for a payment of $100 today and a further $1,300 in
    8 months time. The other option is to pay in full today for a cash price of
    $1,200.

    How can I calculate the effective annual interest rate (assuming monthly
    compounding) being implicitly charged?



  2. #2
    macropod
    Guest

    Re: Effective Annual Interest Rate

    Hi John,

    Technically, there isn't a compounding monthly interest rate for the
    situation you have described, since there's only a single payment, after 8
    months (rather than 8 monthly payments).

    Also, you can only solve for the interest rate through iteration, there
    being no formula for it (unless the periodic payment is zero). In this case,
    the periodic payment (at the 8-month interval) is $200.

    You can calculate an effective annual interest rate (through iteration),
    using Excel's NPER formula and solving for NPER = 1.5, using the Goal Seek
    function.

    Cheers


    "John" <[email protected]> wrote in message
    news:[email protected]...
    > I'm trying to work out the effective annual interest rate for:
    >
    > an item can be purchased for a payment of $100 today and a further $1,300

    in
    > 8 months time. The other option is to pay in full today for a cash price

    of
    > $1,200.
    >
    > How can I calculate the effective annual interest rate (assuming monthly
    > compounding) being implicitly charged?
    >
    >




  3. #3
    Fred Smith
    Guest

    Re: Effective Annual Interest Rate

    You can get your answer by rephrasing your question to: "If I invest $1100
    today, what interest rate will I need to have $1300 in 8 months time?". Use
    the Rate function to get your answer:

    =Rate(8,0,-1100,1300)

    This gives you the monthly rate. To get the effective annual rate, use (with
    the Analysis ToolPak loaded):

    =Effect(rate(8,0,-1100,1300),12)*12

    I get 25.5% as the effective rate. Pay the whole $1200 today.

    --
    Regards,
    Fred
    Please reply to newsgroup, not e-mail


    "John" <[email protected]> wrote in message
    news:[email protected]...
    > I'm trying to work out the effective annual interest rate for:
    >
    > an item can be purchased for a payment of $100 today and a further $1,300
    > in 8 months time. The other option is to pay in full today for a cash
    > price of $1,200.
    >
    > How can I calculate the effective annual interest rate (assuming monthly
    > compounding) being implicitly charged?
    >
    >




  4. #4
    N Harkawat
    Guest

    Re: Effective Annual Interest Rate

    Effective Annual rate is the rate if compounded annually, will yield the
    same amount of interest as if compounded monthly

    So using the function

    =Rate(8,0,-1100,1300)
    will give a monthly rate of 2.11%

    Hence the effective Annual rate

    = ((1+2.11%)^12 )-1

    =28.47%



    Therefore if you financed 1100 today you have to pay 1300 in 8 months and
    1.2847 * 1100 = 1413.17 in 12 months



    Using the effect function that fred suggested we are erroneously dividing
    the monthly rate by 12 and then compounding that

    If 25.5% is the correct annual rate then in 12 months 1100 would be = 1100*
    1.255 = 1380.50

    If in 8 months 1100 increases by 200 to 1300 then how come in next 4 months
    it only increases by 80.5 (from 1300 to 1380.5) whereas it should at least
    increase by 100 ignoring

    the effect of compounding







    "Fred Smith" <[email protected]> wrote in message
    news:eCF0%[email protected]...
    > You can get your answer by rephrasing your question to: "If I invest $1100
    > today, what interest rate will I need to have $1300 in 8 months time?".
    > Use the Rate function to get your answer:
    >
    > =Rate(8,0,-1100,1300)
    >
    > This gives you the monthly rate. To get the effective annual rate, use
    > (with the Analysis ToolPak loaded):
    >
    > =Effect(rate(8,0,-1100,1300),12)*12
    >
    > I get 25.5% as the effective rate. Pay the whole $1200 today.
    >
    > --
    > Regards,
    > Fred
    > Please reply to newsgroup, not e-mail
    >
    >
    > "John" <[email protected]> wrote in message
    > news:[email protected]...
    >> I'm trying to work out the effective annual interest rate for:
    >>
    >> an item can be purchased for a payment of $100 today and a further $1,300
    >> in 8 months time. The other option is to pay in full today for a cash
    >> price of $1,200.
    >>
    >> How can I calculate the effective annual interest rate (assuming monthly
    >> compounding) being implicitly charged?
    >>
    >>

    >
    >




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