1. avatar says

    Mr. Moffat

    After watching your lecture working through the couple of examples you had on calculating the effective interest rate, I used the same examples to calculate the effective interest rate using a formula that the Kaplan text provides to calculate effective rates: r = (1+i/n)^n – 1, where r is the effective interest rate and i is the nominal one, n os the number of time periods. Using that formula to calculate the effective interest for example 4, the formula would have the following numbers: r = (1 + (0.02)/12)^12 – 1 which results in an effective rate of 0.02183 or 2.018% (compared to 26.82% in your answer). I’m assuming that the formula is correct and that I am missing something. Any chance you can spot my mistake?

    Thank you!

    • Profile photo of John Moffat says

      The interest is 2% per month, and so the annual rate is 1.02^12 – 1 = 1.2682 or 26.82%

      (You would only take 0.02/12 if 2% was the yearly rate)

      Think about it – 2% per month could not possible be equivalent to 2.018% per year!!!

  2. avatar says

    Hello Sir, can you please help me with this question?
    Loan taken = £2,000
    Interest reate = 10% per annum.
    The person wishes to make equal monthly repayments comprising interest and principal, over 3 yrs starting one month after the loan is taken out.
    What would be the monthly repayment on the loan?

    Sir can you please explain how to calculate this?
    Thank you

    • Profile photo of John Moffat says

      I don’t know where you got this question from, but I would be very surprised if it would be asked in the exam! :-)

      First you need to calculate the interest rate per month. If the monthly rate is r, then
      (1+r)^12 = 1.10. So r = 0.00797414 (or 0.797414%)

      Then you need to calculate the annuity discount factor for 36 periods, using the formula.
      Which is (1 – 1/((1.00797414)^36))/0.00797414 = 31.18646

      The monthly payment will be the amount of the loan divided by this annuity factor:
      2000 / 31.18646 = $64.13.

      (You had better check my arithmetic :-) )

      Again, I would be very surprised indeed if this were to be asked in a real F2 exam.

      • Profile photo of John Moffat says

        You are welcome.

        And no, although you are not wasting your time looking at the question, they do not ask that sort of question these days.

        In 2002, Paper F2 did not exist – it was a different exam with a different syllabus (more statistical). Also, in 2002 there were no multiple choice questions, whereas now it is entirely multiple choice.

      • avatar says

        Sir, I’m also interested in this question due to nature of my job. How did u arrive at r=0.00797414? Also what is the formula used to get annuity factor 31.8646? Thank you

      • Profile photo of John Moffat says

        For the calculation of 0.00797414, as I wrote in the previous comment (1+r)^12 = 1.10, so 1+r = the 12th root of 1.10.

        The formula for the annuity discount factor is printed at the top of the annuity factor tables that is provided in the exam.

  3. Profile photo of siddiqui93 says

    Hi admin I need your help
    A Co adds interest monthly to investors’ accounts even though interest rates are expressed in annual terms. The current rate of interest is 6% per annum
    An investor deposits $1000 on 1 Jan . How much interest will have been earned by 30 June?

    The correct answer is $30.38
    and I my answer is $ 30

    • Profile photo of John Moffat says

      It depends on the question – there is no rule.

      For example, usually if we are calculating unit costs then we round to the nearest cent. If we are calculating total costs then we usually round to the nearest $.

      For Paper F2, the answers to choose from make it obvious what rounding (if any) is needed. (Or, if you are doing CBE and a question asks you to type in an answer then it will tell you ‘to the nearest $’ or ‘to the nearest $100’ or whatever.

      In later exams where you have to write a full answer rather then just choosing one from four, then unless you are told different then it is usually to the nearest $ for total costs and the nearest cent for unit costs. (Although the markers are sensible – you don’t normally lose marks for rounding unless it is ridiculous)

    • Profile photo of John Moffat says

      Because you put your question under the lecture on interest, for interest rates the choice of answers or the wording of the question will make it clear – sometimes it will be to the nearest % and sometimes it will be to two decimal places.

  4. avatar says

    Hi there,

    Can you please explain this question?
    Hi there,

    Can you please explain this question taken from June 2012 exam paper?

    An investor has the choice between two investments. Investment Exe offers interest of 4% per year compounded semi-annually for a period of three years. Investment Wye offers one interest payment of 20% at the end of its four-year life.
    What is the annual effective interest rate offered by the two investments?
    Investment Exe Investment Wye
    A 4·00%n 4·66%
    B 4·00% 5·00%
    C 4·04% 4·66%
    D 4·04% 5·00%

    The correct answer is C.

      • avatar says

        Ruby, could you write the common formula for annual effective rate? In course notes I found r = (1+i/n)^n -1, where r – effective interest rate,
        i – nominal interest rate, n – number of time periods. But I am a bit confused, because according to the video lecture, the formula is without division into n (i/n)

        Thank you

  5. avatar says

    Hi there,

    Can you please explain this question taken from June 2012 paper?

    An investment centre earns a return on investment of 18% and a residual income of $300,000. The cost of capital is 15%. A new project offers a return on capital employed of 17%. If the new project were adopted, what would happen to the investment centre’s return on investment and residual income?

    Return on investment Residual income
    A increase decrease
    B increase increase
    C decrease decrease
    D decrease increase

    The correct answer is D.


    • avatar says

      New project has ROCE = 17% >> This will make average ROI of the centre decrease
      >>> Profit decreases, Investment increases
      >>> Residual income (= Profit – Interest on investment) also decreases.

      Hope that helps :)

      • avatar says

        Oh I made a mistake. The new project offer a return of 17%, higher than the cost of capital 15%, so the residual income will increase, not decrease.

      • Profile photo of John Moffat says

        Rubydinh’s final answer is correct
        Since 17% is less than the current ROI of 18%, the ROI will decrease.
        Since 17% is greater than the cost of capital of 15%, the RI will increase.

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