From practice question: What is the present value of $6,000 per annum first receivable immediately, and thereafter in perpetuity with an interest rate of 9.5% per annum? Can you explain too me why did we add the $6,000 to the total of $63,158 which gives us a grand total of $69,158 and we did not add the $5,000 in example 9?

Using annuity factors is for equal annual flows that start in 1 years time.

If there is $6,000 receivable immediately, then this is not dealt with by the annuity factor, and so it needs adding on (and obviously the PV of 6,000 is 60,000 🙂 )

They are 8 separate payments. The receipt in 1 year is discounted to remove 1 years interest. The receipt in 2 years is discounted to remove 2 years interest, and so on.

Sir, in the formula for Perpetuity, what does “A” stand for (A/r).

Secondly, I would like to thank you for the logics behind every formula.

Lastly I would like to thankyou for the easy annuity formula you provided (when the receipt starts from between the years), and it’s easy logic. Because the formula provided in my institute book is more complicated.

Your class is like our Emergency S.O.S class lol.

If it wasn’t for my discovery of you and the Kaplan Text books, that I came across by God’s grace, I dread to imagine the quality of progress today.

I was referring to the formula where we minus the annuity factor of the last year with the annuity factor of the year we wish to remove from the calculation, and then multiply this balance of this difference with the FV, to obtain the PV.

Q1) when calculating annuity in Ex.7 of $500 every year. If in 2nd yr $500 additional is added, why should we not total the first year $500 and this second year $500, and then calcluate present value of this total ? {in regards to when you were using the Pv table and not Annuity table).

Q2) The PV answer that you got $2484 for Ex.7, is it possible to reverse calculate and show the working how it gets broken into FV $500 per year for 8 yrs @12% interest p.a ?

hi John, I now know the answer no need to reply, if the perpetuity is paid immediately then we add the initial payment but if it is paid in 1 year’s time then we dont add it on. Thank you

hi John, on the perpetuity question in the mock exam, $41667 do you add the 5000 on top or just $41667 is the correct answer. I have seen the mock question which appears to add the investment amount.

Sir, I wonder if you deposit $41667 in ex-wife’s account so as to fulfill the condition of $5000 a year, then she will receive both principal $41667 and interests $5000. Why don’t u keep it in your account and just give interests to her each year despite you don’t want to make contact.

I mean using above method, she will be received beyond the condition, which is just $5000 a year.

Hello John thank you for the lecture, have you ignored the Advanced annuities and perpetuities (Some regular cash flows may start now (at T0) rather than in one years’ time (T1). and Annuities/Perpetuities in arrears (Some regular cash flows may start later than T1). or they are out of exam syllabus? Please kindly clarify!

Hi John, I wanted to know if we can find example no 8 through the formula for present value or can we only solve this example using the present value annuity table.

In the formula,what value will we take for number of years.Will it be 9 or 12? Because I don’t seem to be the getting the answer using either of it as number of years in the given formula.

You use the annuity factor for 12 years less the annuity factor for 3 years – just as I explain in the lecture.

Whether you get the factors from the tables or you calculate them yourself using the formula doesn’t matter, but it is ridiculous to use the formula when you are given the annuity table in the exam.

It depends on what calculator you have. It will explain in the manual (and if you have lost the manual then you can find it by typing the model number into Google).

However, for 4 years at 10% it makes more sense to use the tables provided in the exam anyway (and I explain how to use the tables in the lectures).

2004@2004 says

Sir, Is 500 a cash inflow or outflow that you have done in the annuity question? Are we investing 500 p.a or receiving it p.a.

mannannagpal says

Hi John! Could you please explain why is putting $2484 in the bank now better than receiving $500 each year for 8 years?

John Moffat says

It isn’t better. It is the same because with interest at 12% we could put $2,484 in the bank now and be able to take out $500 per year for 8 years.

Joanne94 says

Hello Sir, This is probably a silly question but in the workings for annuities example 8 where do you get the 12. (4-12). I don’t get it.

Thank you!

John Moffat says

The first receipt is at time 4. If you count for a total of 9 receipts (including that at time 4) then you find that the last receipt is at time 12.

Joanne94 says

Right. Got it now. Thank you, very much.

John Moffat says

You are welcome 🙂

Alexis says

From practice question: What is the present value of $6,000 per annum first receivable immediately, and thereafter in perpetuity with an interest rate of 9.5% per annum? Can you explain too me why did we add the $6,000 to the total of $63,158 which gives us a grand total of $69,158 and we did not add the $5,000 in example 9?

John Moffat says

Using annuity factors is for equal annual flows that start in 1 years time.

If there is $6,000 receivable immediately, then this is not dealt with by the annuity factor, and so it needs adding on (and obviously the PV of 6,000 is 60,000 🙂 )

Alexis says

Thank you!

jvowles says

Hi,

With example 7, why would you not just do 500/1.12= £446.42 (8 times)?

If its 8 separate £500’s each year with 12% interest each time, why isnt the total PV not 446.42*8= £3571?

Is the interest or 500 changing each year? or are they 8 * 500 separate payments each year?

John Moffat says

They are 8 separate payments. The receipt in 1 year is discounted to remove 1 years interest. The receipt in 2 years is discounted to remove 2 years interest, and so on.

gkumar84@live.com says

Lovely lecture and explanation.

Asif110 says

Sir, in the formula for Perpetuity, what does “A” stand for (A/r).

Secondly, I would like to thank you for the logics behind every formula.

Lastly I would like to thankyou for the easy annuity formula you provided (when the receipt starts from between the years), and it’s easy logic. Because the formula provided in my institute book is more complicated.

Your class is like our Emergency S.O.S class lol.

If it wasn’t for my discovery of you and the Kaplan Text books, that I came across by God’s grace, I dread to imagine the quality of progress today.

John Moffat says

A is the equal annual amount.

Apart from perpetuities it is not so common to need the other formulas – for most question it is more sensible to use the tables provided.

Asif110 says

How is equal annual amount = 1 ?

I was referring to the formula where we minus the annuity factor of the last year with the annuity factor of the year we wish to remove from the calculation, and then multiply this balance of this difference with the FV, to obtain the PV.

Asif110 says

ie the simple formula you used in the video using the Annuity tables.

Asif110 says

Dear Sir,

Q1) when calculating annuity in Ex.7 of $500 every year. If in 2nd yr $500 additional is added, why should we not total the first year $500 and this second year $500, and then calcluate present value of this total ? {in regards to when you were using the Pv table and not Annuity table).

Q2) The PV answer that you got $2484 for Ex.7, is it possible to reverse calculate and show the working how it gets broken into FV $500 per year for 8 yrs @12% interest p.a ?

artipha says

hi John, I now know the answer no need to reply, if the perpetuity is paid immediately then we add the initial payment but if it is paid in 1 year’s time then we dont add it on. Thank you

John Moffat says

Correct 🙂

artipha says

hi John, on the perpetuity question in the mock exam, $41667 do you add the 5000 on top or just $41667 is the correct answer. I have seen the mock question which appears to add the investment amount.

RQ92 says

In the mock question the money is receivable immediately whereas in the lecture question the money is receivable after the first year

John Moffat says

That is correct 🙂

kevinc19 says

Sir, I wonder if you deposit $41667 in ex-wife’s account so as to fulfill the condition of $5000 a year, then she will receive both principal $41667 and interests $5000. Why don’t u keep it in your account and just give interests to her each year despite you don’t want to make contact.

I mean using above method, she will be received beyond the condition, which is just $5000 a year.

John Moffat says

I did not say that I would put the money in her account. I would put it in a separate account which would generate the interest for ever.

rahmatbakhshi says

Hello John thank you for the lecture, have you ignored the Advanced annuities and perpetuities (Some regular cash flows may start now (at T0) rather than in one years’ time (T1). and Annuities/Perpetuities in arrears (Some regular cash flows may start later than T1). or they are out of exam syllabus? Please kindly clarify!

Bebo15 says

Can someone send me the table for discounted factor ?

John Moffat says

The tables are printed in our free lecture notes (you can download the notes free of charge).

Khaula says

Hi John, I wanted to know if we can find example no 8 through the formula for present value or can we only solve this example using the present value annuity table.

John Moffat says

You can do it either way, but it is obviously quicker to use the annuity tables when it is an equal cash flow each year.

Khaula says

In the formula,what value will we take for number of years.Will it be 9 or 12?

Because I don’t seem to be the getting the answer using either of it as number of years in the given formula.

John Moffat says

You use the annuity factor for 12 years less the annuity factor for 3 years – just as I explain in the lecture.

Whether you get the factors from the tables or you calculate them yourself using the formula doesn’t matter, but it is ridiculous to use the formula when you are given the annuity table in the exam.

perrettjoseph says

I have no idea how to write 800 X 1/(1.1)to the power of 4 in a calculator. What am I missing?

John Moffat says

It depends on what calculator you have. It will explain in the manual (and if you have lost the manual then you can find it by typing the model number into Google).

However, for 4 years at 10% it makes more sense to use the tables provided in the exam anyway (and I explain how to use the tables in the lectures).

gkumar84@live.com says

use ^ as a power of any number.

Hope you did.