• Profile photo of John Moffat says

      Discounting is calculating the equivalent amount ‘now’ by removing the interest.

      An annuity is simply an equal cash flow each year. When we discount an annuity we can save time by multiplying by the total of the discount factor (the annuity discount factor) instead of having to discount each cash flow separately using the ordinary discount factors.

  1. avatar says

    Hello Sir,

    Question 4 in the test questions asks for the present value of $2000 per annum first receivable in 3 YEARS,but the solutions at the end of the notes calculates the first receipt after 2 YEARS.
    Please could you shed more light on this and give clarity as to why they are different using the different number of years gives different answers. Or am I missing something or got something wrong somewhere? Please help.

    Many thanks.

  2. Profile photo of Imran says

    Hey John, in annuity, i just wanted to knew if there was an easier way of calculating the
    “total Annuity discount factor” i kind of calculate each and every year one by one and then total them all, it is really lengthy and exhausting. any idea? and thanks the lectures are just awesome!

  3. avatar says

    hi John;
    i’d like to thank you for this lecture .it is very helpfull ..
    ive been trought some of the videos but i still dint get the 0.893 in this video above or on the payback period video the 0.909 figure.. could you kindly explain that to as im getting stucked on that.. thks MAX

  4. avatar says

    Hi John,
    Quick question about perpetuities. I know how to calculate a perpetuity that starts now, but in a practice exam it said that payments would begin in 4 years time. Do I need to discount for years 1-3 and if so, how would I do that?

    Thanks for your help.

    • Profile photo of John Moffat says

      There two ways that both give the same answer.

      Either use 1/r for the perpetuity, and then discount for a further three years using the normal discount factor for three years.


      Use 1/r for the perpetuity, and then subtract the three year annuity discount factor ( so as to be left with 4 to infinity)

      Both will give the same answer. (Except for rounding difference)

    • Profile photo of John Moffat says

      What you get in the exam is the formula sheet and the present value tables. You will see that at the top of the present value tables there are the formulae for the discount factors (both normal discount factors and annuity factors).

      You get these sheets in the exam.

  5. avatar says

    Hi John,

    Thank you for your brilliant lectures. I seem to be having trouble understanding example 8. Am i wrong in thinking that the question is asking for this -> “What amount of money should be invested TODAY so that in 4 year’s time from TODAY, you can start to withdraw $1000 each year for 9 consecutive years”?

    Using the annuity table/formula, in order to receive $1000 for 9 years at a discount rate 8%, you would need to invest $1000 x 6.247 = $6247. I assume when the question says “4 years time”, it means that TODAY’s money would be invested for 4 complete years, making the present value of the $6247 (at 8% d/r) = $6247 x 0.735 = $4591.60

    What am i missing? Or have i cocked up completely :S

    Thank you!

    • Profile photo of John Moffat says

      What you have written is correct, except for one thing.

      If the flows had been from time 1 to time 9, then multiplying by the 9 year annuity factor would give a present value (i.e. an amount at time 0).

      Here, the flows are from time 4 to time 12 – everything is 3 years later, and so multiplying by the annuity factor gives an amount three years later i.e. at time 3.
      So to get a present value we need to discount for 3 years (not 4 years).

      $6247 x 0.794 (three year DF at 8%) = $4960 (which is the correct answer).

      (There are two approaches you can use to get the same answer – the other approach is shown in the answer at the back of the course notes)

  6. avatar says

    I Mr.Moffat

    I would like to know i for CBE where i am ask to select three answers for the same question and if two is right and one wrong are if i choose two and leave one will i get 1/2 mark for the question.

  7. Profile photo of abdullahtabba says

    An Investor Is to recieve annuity of $19260 for six year commencing at end of year 1 it has a present value of $86400.
    what is a rate of intrest??
    Answer with The Manual Calculation OF Rate OF intrest Without Using Table

  8. avatar says

    hi guys pliz hlp me on this que. dont know how to solve it.

    Mr Mannaton has recently won a competition where he has the choice between receiving $5000 now or an annual amount forever starting now. (ie a level perpertuity starting immediately). the interest rate is 8% per annum. what would be the value of perpetuity to the nearest $?

    • avatar says

      Hi there

      the perpertual annuity formula that i know is P = R over i where P is Present value and the R is payments and i is the interest. Now i think we can play with mathematics here and say since we know the present value we can multiply it by the interest to get the R which is the payments value $ 5000 x 0.08 = $400
      so $400 will be the monthly payments to be recieved indefinitely

      • Profile photo of John Moffat says

        Not quite.
        The question says that the perpetuity starts immediately – i.e. the first receipt is at time 0 (or now).

        So…..if x is the amount per annum, then (5000 – x ).0.08 = x
        400 – 0.08x = x
        400 = 1.08x
        So x = 400 / 1.08 = 370.38 p.a.

    • Profile photo of John Moffat says

      @accakeisha, I am not sure which example you are referring to – there are many in this lecture.
      If you mean the one that says $5,000 is first received in 3 years time, and that there are 12 receipts in total, then my arithmetic is correct!
      The first receipt is in 3 year, the second in 4 years, the third in 5 years….if you carry on the the 12th receipt is in 14 years time.

    • Profile photo of John Moffat says

      @claudette, it is because we want the total factor for years 3 to 14 inclusive.

      The 14 year factor gives the total for years 1 to 14, so we need to take off the total for years 1 and 2 (the 2 year annuity factor) to be left with the total for 3 to 14.

  9. Profile photo of John Moffat says

    Hi Jide

    There is a tiny typing error in the first line of the answer (thank you for noticing it – I will have it corrected immediately).

    The first line should read “The first receipt is in 3 years time and the last receipt is in 10 years time”.

    Everything else in the answer is correct – we take the annuity d.f. for 10 years, and subtract the annuity d.f. for 2 years, so as to be left with the total d.f. for years 3 to 10.

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