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Present Value

Consider an ordinary annuity whereby an investor is paid £1000 at the end of each year for 10 years. What is the present value of the annuity if annual interest rate is 6% per year?

Is this just 1000(1.06)^10 = 1790.85?
Original post by Deannnn97
Consider an ordinary annuity whereby an investor is paid £1000 at the end of each year for 10 years. What is the present value of the annuity if annual interest rate is 6% per year?

Is this just 1000(1.06)^10 = 1790.85?


Not quite. Try breaking it up into 10 different future values (that are all £1000) and calculate their worth today. Eg £1000 at the end of this year.. to be honest, I never know with these questions - whether say, at the end of 2016, you have £1000 or £1060 or whether you only get £1060 on the 1st of Jan.

But anyway, once you work that out, you've got your future values (all £1000) but you have to discount them differently. Eg 10th payment which is £1000 has a PV of .... and I'm sure you can apply a sum formula once you've worked out what it is that you have to calculate.
Reply 2
Avatar for Deannnn97
Deannnn97
OP
Original post by SeanFM
Not quite. Try breaking it up into 10 different future values (that are all £1000) and calculate their worth today. Eg £1000 at the end of this year.. to be honest, I never know with these questions - whether say, at the end of 2016, you have £1000 or £1060 or whether you only get £1060 on the 1st of Jan.

But anyway, once you work that out, you've got your future values (all £1000) but you have to discount them differently. Eg 10th payment which is £1000 has a PV of .... and I'm sure you can apply a sum formula once you've worked out what it is that you have to calculate.


Thanks so:
1000(1.06)^1 = ... 1000(1.06)^2 = ... 1000(1.06)^3 = ....... until 1000(1.06)^10 and then add all these together?
Original post by Deannnn97
Thanks so:
1000(1.06)^1 = ... 1000(1.06)^2 = ... 1000(1.06)^3 = ....... until 1000(1.06)^10 and then add all these together?


Not quite - you're doing the opposite of what you should be doing, but with the right idea.

It is the opposite because you are turning things into Future Values, so you would be summing up the future values of a £1000 annuity.

But the question requries the present value.
Original post by Deannnn97
Consider an ordinary annuity whereby an investor is paid £1000 at the end of each year for 10 years. What is the present value of the annuity if annual interest rate is 6% per year?

Is this just 1000(1.06)^10 = 1790.85?


Surely it would just be 1000(1.06)⋅101000(1.06)\cdot10

Every year he gets 1000 at the rate of 6% for 10 years... unless im misunderstanding.

The exponent is not needed because he doesn't invest anything back so his stock remains the same, so to speak, if his fixed gain is 1000 per year.
(edited 7 years ago)
Reply 5
Avatar for Deannnn97
Deannnn97
OP
Original post by SeanFM
Not quite - you're doing the opposite of what you should be doing, but with the right idea.

It is the opposite because you are turning things into Future Values, so you would be summing up the future values of a £1000 annuity.

But the question requries the present value.


Haha im so confused, so what is the answer? I could then figure out how to do it easier, as I will keep going through the different methods I know until one gives me the same answer as you.
Original post by Deannnn97
Haha im so confused, so what is the answer? I could then figure out how to do it easier, as I will keep going through the different methods I know until one gives me the same answer as you.


If you are paid £1000 at the end of this year, how much is it worth today? (PV) Assume interest gets paid on the 1st of January.

The answer as far as I am aware is £1000.

Now, you are paid another £1000 1 year later, but that is the future value that is being paid. That is the key bit. They're not saying 'I'm going to pay you £1000 worth in terms of today's money every year', they're saying that they're going to pay you £1000 even though the value of £1000 in 10 years with an interest rate of 1.06 is fairly low. So your second £1000 is worth how much now? How about the 3rd? What's the pattern?
Reply 7
Avatar for Deannnn97
Deannnn97
OP
Original post by SeanFM
If you are paid £1000 at the end of this year, how much is it worth today? (PV) Assume interest gets paid on the 1st of January.

The answer as far as I am aware is £1000.

Now, you are paid another £1000 1 year later, but that is the future value that is being paid. That is the key bit. They're not saying 'I'm going to pay you £1000 worth in terms of today's money every year', they're saying that they're going to pay you £1000 even though the value of £1000 in 10 years with an interest rate of 1.06 is fairly low. So your second £1000 is worth how much now? How about the 3rd? What's the pattern?


Ok thanks i get it now
:smile:

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