Mixing
Deferred Term-Limited Annuity
$begingroup$
I'm looking for a formula to calculate the EPV of an annuity (in terms of $a_x $ , $ a_{xy} $ etc) that is payable during life y, for a maximum of n years, but only beginning on the death of life x.
I can work out the EPV of a deferred unlimited annuity - it's simply $ a_y - a_{xy} $. Intuitively that's life y receiving an annuity, but "paying it back" as long as he and life x are still living.
I can also solve it for a guaranteed annuity payable on death of life x. That's simply $ a_{10}| $ * $ A_x $.
Here, however, the present value of the annuity varies depending on the lifetime of x and relies on life y being alive, so it's more complicated.
Is there some kind of intuitive answer to this?
actuarial-science
asked Feb 2 at 22:15
AKAAKA
84
$endgroup$
add a comment |
$begingroup$
I'm looking for a formula to calculate the EPV of an annuity (in terms of $a_x $ , $ a_{xy} $ etc) that is payable during life y, for a maximum of n years, but only beginning on the death of life x.
I can work out the EPV of a deferred unlimited annuity - it's simply $ a_y - a_{xy} $. Intuitively that's life y receiving an annuity, but "paying it back" as long as he and life x are still living.
I can also solve it for a guaranteed annuity payable on death of life x. That's simply $ a_{10}| $ * $ A_x $.
Here, however, the present value of the annuity varies depending on the lifetime of x and relies on life y being alive, so it's more complicated.
Is there some kind of intuitive answer to this?
actuarial-science
asked Feb 2 at 22:15
AKAAKA
84
$endgroup$
$begingroup$
If the annuity were payable during the life of $y$ but for no more than $10$ years, the present value would be an immediate life annuity to $y$ minus a ten-year deferred annuity to $y.$ I don't remember the notation. I think you can expand on this to get the joint annuity.
$endgroup$
– saulspatz
Feb 2 at 22:54
add a comment |
$begingroup$
I'm looking for a formula to calculate the EPV of an annuity (in terms of $a_x $ , $ a_{xy} $ etc) that is payable during life y, for a maximum of n years, but only beginning on the death of life x.
I can work out the EPV of a deferred unlimited annuity - it's simply $ a_y - a_{xy} $. Intuitively that's life y receiving an annuity, but "paying it back" as long as he and life x are still living.
I can also solve it for a guaranteed annuity payable on death of life x. That's simply $ a_{10}| $ * $ A_x $.
Here, however, the present value of the annuity varies depending on the lifetime of x and relies on life y being alive, so it's more complicated.
Is there some kind of intuitive answer to this?
actuarial-science
asked Feb 2 at 22:15
AKAAKA
84
$endgroup$
I'm looking for a formula to calculate the EPV of an annuity (in terms of $a_x $ , $ a_{xy} $ etc) that is payable during life y, for a maximum of n years, but only beginning on the death of life x.
I can work out the EPV of a deferred unlimited annuity - it's simply $ a_y - a_{xy} $. Intuitively that's life y receiving an annuity, but "paying it back" as long as he and life x are still living.
I can also solve it for a guaranteed annuity payable on death of life x. That's simply $ a_{10}| $ * $ A_x $.
Here, however, the present value of the annuity varies depending on the lifetime of x and relies on life y being alive, so it's more complicated.
Is there some kind of intuitive answer to this?
actuarial-science
actuarial-science
asked Feb 2 at 22:15
AKAAKA
84
asked Feb 2 at 22:15
AKAAKA
84
asked Feb 2 at 22:15
AKAAKA
84
asked Feb 2 at 22:15
AKAAKA
84
asked Feb 2 at 22:15
AKAAKA
84
84
$begingroup$
If the annuity were payable during the life of $y$ but for no more than $10$ years, the present value would be an immediate life annuity to $y$ minus a ten-year deferred annuity to $y.$ I don't remember the notation. I think you can expand on this to get the joint annuity.
$endgroup$
– saulspatz
Feb 2 at 22:54
add a comment |
$begingroup$
If the annuity were payable during the life of $y$ but for no more than $10$ years, the present value would be an immediate life annuity to $y$ minus a ten-year deferred annuity to $y.$ I don't remember the notation. I think you can expand on this to get the joint annuity.
$endgroup$
– saulspatz
Feb 2 at 22:54
$begingroup$
If the annuity were payable during the life of $y$ but for no more than $10$ years, the present value would be an immediate life annuity to $y$ minus a ten-year deferred annuity to $y.$ I don't remember the notation. I think you can expand on this to get the joint annuity.
$endgroup$
– saulspatz
Feb 2 at 22:54
$begingroup$
If the annuity were payable during the life of $y$ but for no more than $10$ years, the present value would be an immediate life annuity to $y$ minus a ten-year deferred annuity to $y.$ I don't remember the notation. I think you can expand on this to get the joint annuity.
$endgroup$
– saulspatz
Feb 2 at 22:54
add a comment |
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$begingroup$
If the annuity were payable during the life of $y$ but for no more than $10$ years, the present value would be an immediate life annuity to $y$ minus a ten-year deferred annuity to $y.$ I don't remember the notation. I think you can expand on this to get the joint annuity.
$endgroup$
– saulspatz
Feb 2 at 22:54