# Interest Annuities Example 7

1. 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.

• 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.

2. 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.

• 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.

3. 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!

• 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)

4. 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

• says

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

• 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.

5. 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?

• 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)

• 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.

6. 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!

• 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)

• says

Fantastic thank you for the explanation That makes more sense.

7. 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?

• 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.

8. 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.

• says

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

9. 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?

• 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 )

10. 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

• 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.

• says

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

• 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).

11. says

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

12. 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

• 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).

• says

do they give annuity table in the exam or not

• says

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

13. 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 \$?

• 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

• 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.

14. 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

• 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.

15. says

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

• 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.

16. 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.

17. says

Hello Mr John Moffat,

Ok then, no problem.