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Nhat Anh says

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

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

SH says

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.

John Moffat says

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.

jeevasaeyan says

Hi John,

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!

John Moffat says

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? 🙂

Sammar says

$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??

Sammar says

2484 ÷ 8 = 310.5

1516 ÷ 8 = 189.5

So the total amount we get every year is 500

John Moffat says

$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.

Carol says

Where can I find the lecture on Perpetuities?

John Moffat says

Here:

http://opentuition.com/acca/f2/acca-f2-revision-part-8b-discounting-compounding-interest-investment-appraisal/

Carol says

Thank you!

Emily says

sir how did you get the 4,968

John Moffat says

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

Julian says

Hi John

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!)

Many thanks

Julian

John Moffat says

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).

gg says

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

John Moffat says

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.

IMEH says

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.

Thanks.

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.

Jide 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.

Raj Singh says

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.

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!

John Moffat says

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

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

John Moffat says

Have you looked at the answers to the examples at the end of the Course Notes?

Max Huelber says

nope…where do i find it??? im new to this ….thks

John Moffat says

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.

Emily says

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

John Moffat says

If you look at the discount tables, then the 1 year factor at 12% is 0.893.

Neil 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.

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.

Or

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)

Emil says

Will annuities formula be given in exam?

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.

Mohammed 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!

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)

Mohammed says

Fantastic thank you for the explanation 🙂 That makes more sense.

abhinandh dileep says

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?

John Moffat says

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.

abhinandh dileep says

thanks a lot…

Antoinette 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.

John Moffat says

With CBE you get full marks if the whole answer is correct, and no marks if the whole answer is not correct.

tijani says

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?

John Moffat says

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 )

amberly124 says

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

John Moffat says

The present value tables and the annuity tables are both given in the exam.

salome1 says

Will these formulas (annuity and present value) be given in exam papers?

John Moffat says

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.

salome1 says

okey, may they check us if we know formula for present value of annuity, may they give e.g. 5.3% or sth?

John Moffat says

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).

salome1 says

thank you very much 🙂

elizabeth says

for the last question was lost because i dont have the question nor table……but over all its clearer

carlynspringer says

Must try googling the tables

John Moffat says

The question and the tables are in our course notes!

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

John Moffat says

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).

amberly124 says

do they give annuity table in the exam or not

John Moffat says

The present value tables and the annuity tables are both given in the exam.

esther1986 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 $?

time2009 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

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.

accakeisha says

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

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.

hixam says

Why its the the OT F2 Notes beck answer for question 8 is different of what sir have explained? Its printing mistakes right?

claudette says

why is it 14 years less 2. thanks Teacher you are the best

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.

nhs14 says

is the Fisher’s Price Index equally important as the above???

John Moffat says

@nhs14, well not really, and it has nothing to do with annuities 🙂

mellen says

it’s very sad to see students remain passive in most lectures.

chandhini says

@mellen, It really is frustrating! :/