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Nhat Anh says
October 25, 2016 at 9:30 am
An investment offers one interest payment of 20% at the end of its four-year life. What is the annual effective interest rate offered by this investment?
Sir, help me to find the answer.
John Moffat says
October 25, 2016 at 3:15 pm
In future ask this sort of question in the Ask the Tutor Forum and not as a comment on a lecture!
If R is the annual interest rate, then (1+R)^4 = 1.20
(it is to the power 4 because it is four years).
So R = (fourth root of 1.20) – 1
July 24, 2016 at 3:29 pm
Hello John. Thank you so much for your wonderful lectures. I’ve been enjoying them very mcuh. I have a one small problem though. I cannot find annuity tables anywhere on the lecture note. They are not there any longer or have I missed them? Many thanks.
July 24, 2016 at 8:21 pm
Thank you for the comment 🙂
The tables and formula sheet have been missed by accident – I am sorry and I will have them included immediately. Thank you for noticing.
July 24, 2016 at 4:14 am
Lecture was awesome. My feedback is that if you had used the term “Cash Flows” it would have been more or less clearer.
ie: Cash Flows from year 4 to 12.
Thanks for your lectures!
July 24, 2016 at 7:42 am
Thank you for your comment.
The questions does say they “expect to receive $1,000 a year”, so what else would they receive but cash? 🙂
October 28, 2015 at 5:23 am
$2484 is the amount we put into the bank or whatever, 4000 is the Total we would get in 8 years and the interest we get is 1516,is this right??
October 28, 2015 at 5:26 am
2484 ÷ 8 = 310.5
1516 ÷ 8 = 189.5
So the total amount we get every year is 500
October 28, 2015 at 7:36 am
$2484 is the equivalent amount now.
Certainly if that were the case then the total interest would be 1516, but it would not be 189.5 a year.
If the first year it would earn interest of 12% x 2484, bringing the total to 2782.08
Then we take $500 out, so in the second year it earns interest of 12% x (2782.08 – 500), which brings the total to 2555.93.
Then we take 500 out, and so on.
The only reason your two figures add up to 500 is because in total you have dividend 4000 by 8.
March 29, 2015 at 11:03 pm
Where can I find the lecture on Perpetuities?
March 30, 2015 at 7:28 am
March 30, 2015 at 4:31 pm
June 19, 2015 at 9:50 am
sir how did you get the 4,968
June 19, 2015 at 10:16 am
I used the annuity tables that are printed in the lecture notes (and provided in the exam).
If you look at the 12% column and the 8 year row, then you will find the annuity factor of 4.968
October 23, 2014 at 9:53 pm
Thank you for posting these lectures. I got scribbling whilst you and Inusa were chatting about sneaking a look at the answers in this lecture…
For the question… an annuity of £1k pa. is received for 9 years with the first receipt in 4 years time (at 8%) – I used the tables to calculate a 9 year anuity (cost £6,247), and then used discount factoring to work out what to pay in at 8% to get that amount in 3 years, and got the answer £4,960, which was only £1 away from your answer. I though that this might be an acceptable alternative method, but then in your second example of that type of question, where £5k is received for 12 years with the first receipt in 3 years time (also at 8%), I got a 12 year anuity costing £37,680, requiring a PV of £32,292 (i.e 2 years discount factoring at 8%), which is £7 out from your results. I’m happy to go with your method in the exams, but don’t see why mine shouldn’t work also? Can you comment – is the discrepancy due maybe to the discount and annuity tables being presented to 3dp, or is it something else? (I realise I could work it out longhand to check… perhaps I will do in due course, but the exams are in 6 weeks time and I’ve a lot of material to cover before December!)
October 24, 2014 at 7:20 am
You are correct in that the difference is due to the tables being only to 3 decimal places – it is simply a rounding difference.
In the exam you can use either method – whichever you are most happy with (you do not lose marks because of roundings due to the tables – to avoid this, questions will ask for the answer to the nearest $10 or $100).
January 11, 2016 at 4:47 am
For second question ..how to count to be 14 ? Question said that $ 5 k for the first time 3 year then totally 12 … so first time is 3 , second time is 9 then will be start from 10 , 11, 12 ,13,14,15,16,17,18,19,20,21,22 …. i dont know why teacher said that 14 ? let me be cleared . Thanks John or julia
January 11, 2016 at 9:11 am
The question says it is $5,000 per year – not $5,000 every 3 years!
So the first receipt is in 3 years time, the second is in 4 years time, the third is in 5 years time and so on. The twelfth receipt will be in 14 years time.
October 7, 2014 at 12:58 am
Hello Mr Moffat
Thanks for the lecture.
Please I’d like to know the difference between discounting and annuities; cos I’m actually beginning to get confused.
October 7, 2014 at 8:14 am
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.
August 22, 2014 at 3:10 pm
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.
Raj Singh says
October 15, 2014 at 11:12 pm
Its just a typo. The first line of the solution says 2 years but it should say “the first receipt is in 3 years and last receipt is in 10 years”. However the rest of the working is correct.
July 21, 2014 at 6:47 pm
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!
July 21, 2014 at 7:50 pm
You are given the annuity factors table in the exam (they are printed at the beginning of our course notes, along with the normal present value tables)
Max Huelber says
July 2, 2014 at 6:10 pm
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
July 2, 2014 at 6:13 pm
Have you looked at the answers to the examples at the end of the Course Notes?
July 3, 2014 at 6:49 pm
nope…where do i find it??? im new to this ….thks
July 3, 2014 at 8:46 pm
If you look just above the lecture, on the right, you will see a link to the download the Course Notes.
As it says, you need these to be able to follow the lectures.
At he back of the Course Notes you will find answers to all of the examples.
July 13, 2015 at 6:48 pm
hello sir, I looked at the answers at the back of the course notes and I still don’t understand how u got 0,893…..mind explaining it to me
July 14, 2015 at 9:18 am
If you look at the discount tables, then the 1 year factor at 12% is 0.893.
June 5, 2014 at 12:26 am
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.
June 5, 2014 at 7:04 am
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)
February 25, 2014 at 6:30 pm
Will annuities formula be given in exam?
February 25, 2014 at 6:31 pm
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.
February 13, 2014 at 8:53 am
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
February 13, 2014 at 9:05 am
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)
February 13, 2014 at 9:28 am
Fantastic thank you for the explanation 🙂 That makes more sense.
abhinandh dileep says
December 6, 2013 at 8:33 pm
sir… can you please explain annuity with a an example ? i understood how to calculate it… but i am not able to understand why do we calculate it for?
December 6, 2013 at 11:05 pm
It is explained with examples in all the lectures.
All am annuity is is an equal amount each year. You could discount each year separately, but because it is an equal amount each year it is quicker to use the total of the discount factors for each year, which is all the annuity factors are – the total of the discount factors for each year separately.
December 7, 2013 at 11:45 am
thanks a lot…
November 27, 2013 at 6:44 pm
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.
November 27, 2013 at 10:12 pm
With CBE you get full marks if the whole answer is correct, and no marks if the whole answer is not correct.
October 9, 2013 at 5:14 am
Is perpetuity examinable? There is no lecture on that topic but it is in the notes
My calculator can not calculate the formula (pricipal xx=====………) why?
October 9, 2013 at 5:40 am
Yes – perpetuities are examinable. The discount factor is 1/r where r is the rate of interest. (I do not know which formula your calculator is having problems with )
October 8, 2013 at 2:47 pm
i want to know do they give annuities value like 10% of 1 year have 0.990 then 2nd of etc ,
i should i have to learn or do they give this all
October 8, 2013 at 2:59 pm
The present value tables and the annuity tables are both given in the exam.
June 9, 2013 at 9:07 am
Will these formulas (annuity and present value) be given in exam papers?
June 9, 2013 at 10:01 am
It depends what you mean by the formulae.
The formulae for the discount factors are given at the top of the discount tables, which you are give in the exam.
June 9, 2013 at 10:51 am
okey, may they check us if we know formula for present value of annuity, may they give e.g. 5.3% or sth?
June 9, 2013 at 10:57 am
They can ask you to calculate a discount fact at 5.3% using the formula. However you are not expected to learn the formula – it is given to you at the top of the discount tables (there is copy of them in our course notes).
June 9, 2013 at 11:21 am
thank you very much 🙂
May 17, 2013 at 3:47 am
for the last question was lost because i dont have the question nor table……but over all its clearer
May 20, 2013 at 10:09 pm
Must try googling the tables
May 21, 2013 at 6:02 am
The question and the tables are in our course notes!
February 6, 2013 at 7:26 am
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
April 4, 2013 at 12:27 pm
To answer this without tables would be wasting time – it cannot be asked in Paper F2 (you cannot be asked for manual calculations of this sort).
October 8, 2013 at 2:50 pm
do they give annuity table in the exam or not
January 16, 2013 at 12:45 pm
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 $?
April 3, 2013 at 8:48 pm
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
April 4, 2013 at 12:25 pm
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.
December 11, 2012 at 5:51 pm
from my calculations it is 15 yrs time and not 14 please double check your arithmetic and let me know if i am right or wrong
December 12, 2012 at 6:55 pm
@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.
November 5, 2012 at 10:07 pm
Why its the the OT F2 Notes beck answer for question 8 is different of what sir have explained? Its printing mistakes right?
October 23, 2012 at 2:17 pm
why is it 14 years less 2. thanks Teacher you are the best
October 23, 2012 at 7:47 pm
@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.
October 15, 2012 at 1:20 pm
is the Fisher’s Price Index equally important as the above???
October 23, 2012 at 7:39 pm
@nhs14, well not really, and it has nothing to do with annuities 🙂
July 15, 2012 at 5:05 pm
it’s very sad to see students remain passive in most lectures.
November 24, 2012 at 8:01 am
@mellen, It really is frustrating! :/
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