Why is the calculator giving me different answers???
$begingroup$
I have a question with regards to calculating annuity due in terms of annuity immediate.
I thought that one way to do so is annuity due for n periods = annuity immediate n-1 periods + 1 (where the payment is 1). However, I did this for a part of a problem that is basically
Present value is 500,000 of a 10 year annuity due of X. Interest rate is 9% annual effective. Calculate X. Why doesn’t the following work??
PV of annuity due of 10 years of payment 1 = annuity immediate of 9 years of payment 1 + 1
Then divide 500,000 by the right hand side of this equation?
When I do this, I get PV = 7 from the calculator, so payment is 500,000/7. But when I do another method, I get a lower answer, which is the right answer according to the manual. But I don’t understand why they should be different.
The other method is PV of annuity due of n years = (1 + i) * PV annuity immediate of n years. This gives the correct answer. >.<
Sorry if I’ve misunderstood something fundamental and thank you in advance for the help!
finance actuarial-science
asked Jan 11 at 14:27
quietkidquietkid
415
$endgroup$
add a comment |
$begingroup$
I have a question with regards to calculating annuity due in terms of annuity immediate.
I thought that one way to do so is annuity due for n periods = annuity immediate n-1 periods + 1 (where the payment is 1). However, I did this for a part of a problem that is basically
Present value is 500,000 of a 10 year annuity due of X. Interest rate is 9% annual effective. Calculate X. Why doesn’t the following work??
PV of annuity due of 10 years of payment 1 = annuity immediate of 9 years of payment 1 + 1
Then divide 500,000 by the right hand side of this equation?
When I do this, I get PV = 7 from the calculator, so payment is 500,000/7. But when I do another method, I get a lower answer, which is the right answer according to the manual. But I don’t understand why they should be different.
The other method is PV of annuity due of n years = (1 + i) * PV annuity immediate of n years. This gives the correct answer. >.<
Sorry if I’ve misunderstood something fundamental and thank you in advance for the help!
finance actuarial-science
asked Jan 11 at 14:27
quietkidquietkid
415
$endgroup$
$begingroup$
Please also show the other method.
$endgroup$
– Peter
Jan 11 at 14:35
$begingroup$
It’s edited now, thanks!
$endgroup$
– quietkid
Jan 11 at 14:48
$begingroup$
@quietkid Since you know how to use MathJax I would recommend to write the equations in Mathjax. At the moment it is not clear which equations you´re talking about.
$endgroup$
– callculus
Jan 11 at 17:51
add a comment |
$begingroup$
I have a question with regards to calculating annuity due in terms of annuity immediate.
I thought that one way to do so is annuity due for n periods = annuity immediate n-1 periods + 1 (where the payment is 1). However, I did this for a part of a problem that is basically
Present value is 500,000 of a 10 year annuity due of X. Interest rate is 9% annual effective. Calculate X. Why doesn’t the following work??
PV of annuity due of 10 years of payment 1 = annuity immediate of 9 years of payment 1 + 1
Then divide 500,000 by the right hand side of this equation?
When I do this, I get PV = 7 from the calculator, so payment is 500,000/7. But when I do another method, I get a lower answer, which is the right answer according to the manual. But I don’t understand why they should be different.
The other method is PV of annuity due of n years = (1 + i) * PV annuity immediate of n years. This gives the correct answer. >.<
Sorry if I’ve misunderstood something fundamental and thank you in advance for the help!
finance actuarial-science
asked Jan 11 at 14:27
quietkidquietkid
415
$endgroup$
I have a question with regards to calculating annuity due in terms of annuity immediate.
I thought that one way to do so is annuity due for n periods = annuity immediate n-1 periods + 1 (where the payment is 1). However, I did this for a part of a problem that is basically
Present value is 500,000 of a 10 year annuity due of X. Interest rate is 9% annual effective. Calculate X. Why doesn’t the following work??
PV of annuity due of 10 years of payment 1 = annuity immediate of 9 years of payment 1 + 1
Then divide 500,000 by the right hand side of this equation?
When I do this, I get PV = 7 from the calculator, so payment is 500,000/7. But when I do another method, I get a lower answer, which is the right answer according to the manual. But I don’t understand why they should be different.
The other method is PV of annuity due of n years = (1 + i) * PV annuity immediate of n years. This gives the correct answer. >.<
Sorry if I’ve misunderstood something fundamental and thank you in advance for the help!
finance actuarial-science
finance actuarial-science
asked Jan 11 at 14:27
quietkidquietkid
415
asked Jan 11 at 14:27
quietkidquietkid
415
edited Jan 11 at 14:48
quietkid
asked Jan 11 at 14:27
quietkidquietkid
415
asked Jan 11 at 14:27
quietkidquietkid
415
asked Jan 11 at 14:27
quietkidquietkid
415
415
$begingroup$
Please also show the other method.
$endgroup$
– Peter
Jan 11 at 14:35
$begingroup$
It’s edited now, thanks!
$endgroup$
– quietkid
Jan 11 at 14:48
$begingroup$
@quietkid Since you know how to use MathJax I would recommend to write the equations in Mathjax. At the moment it is not clear which equations you´re talking about.
$endgroup$
– callculus
Jan 11 at 17:51
add a comment |
$begingroup$
Please also show the other method.
$endgroup$
– Peter
Jan 11 at 14:35
$begingroup$
It’s edited now, thanks!
$endgroup$
– quietkid
Jan 11 at 14:48
$begingroup$
@quietkid Since you know how to use MathJax I would recommend to write the equations in Mathjax. At the moment it is not clear which equations you´re talking about.
$endgroup$
– callculus
Jan 11 at 17:51
$begingroup$
Please also show the other method.
$endgroup$
– Peter
Jan 11 at 14:35
$begingroup$
Please also show the other method.
$endgroup$
– Peter
Jan 11 at 14:35
$begingroup$
It’s edited now, thanks!
$endgroup$
– quietkid
Jan 11 at 14:48
$begingroup$
It’s edited now, thanks!
$endgroup$
– quietkid
Jan 11 at 14:48
$begingroup$
@quietkid Since you know how to use MathJax I would recommend to write the equations in Mathjax. At the moment it is not clear which equations you´re talking about.
$endgroup$
– callculus
Jan 11 at 17:51
$begingroup$
@quietkid Since you know how to use MathJax I would recommend to write the equations in Mathjax. At the moment it is not clear which equations you´re talking about.
$endgroup$
– callculus
Jan 11 at 17:51
add a comment |
1 Answer
1
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$begingroup$
You cannot have different results, because
$$
ddot a_{overline{n} |i} =a_{overline{n-1} |i}+i=frac{1-(1+i)^{-(n-1)}}{i} +1=frac{1+i-(1+i)^{-n+1}}{i}=(1+i) frac{1-(1+i)^{-n}}{i}=(1+i)a_{overline{n} |i}
$$
answered Jan 12 at 1:20
alexjoalexjo
12.5k1430
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add a comment |
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1 Answer
1
active
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1 Answer
1
active
oldest
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$begingroup$
You cannot have different results, because
$$
ddot a_{overline{n} |i} =a_{overline{n-1} |i}+i=frac{1-(1+i)^{-(n-1)}}{i} +1=frac{1+i-(1+i)^{-n+1}}{i}=(1+i) frac{1-(1+i)^{-n}}{i}=(1+i)a_{overline{n} |i}
$$
answered Jan 12 at 1:20
alexjoalexjo
12.5k1430
$endgroup$
add a comment |
$begingroup$
You cannot have different results, because
$$
ddot a_{overline{n} |i} =a_{overline{n-1} |i}+i=frac{1-(1+i)^{-(n-1)}}{i} +1=frac{1+i-(1+i)^{-n+1}}{i}=(1+i) frac{1-(1+i)^{-n}}{i}=(1+i)a_{overline{n} |i}
$$
answered Jan 12 at 1:20
alexjoalexjo
12.5k1430
$endgroup$
add a comment |
$begingroup$
You cannot have different results, because
$$
ddot a_{overline{n} |i} =a_{overline{n-1} |i}+i=frac{1-(1+i)^{-(n-1)}}{i} +1=frac{1+i-(1+i)^{-n+1}}{i}=(1+i) frac{1-(1+i)^{-n}}{i}=(1+i)a_{overline{n} |i}
$$
answered Jan 12 at 1:20
alexjoalexjo
12.5k1430
$endgroup$
You cannot have different results, because
$$
ddot a_{overline{n} |i} =a_{overline{n-1} |i}+i=frac{1-(1+i)^{-(n-1)}}{i} +1=frac{1+i-(1+i)^{-n+1}}{i}=(1+i) frac{1-(1+i)^{-n}}{i}=(1+i)a_{overline{n} |i}
$$
answered Jan 12 at 1:20
alexjoalexjo
12.5k1430
answered Jan 12 at 1:20
alexjoalexjo
12.5k1430
answered Jan 12 at 1:20
alexjoalexjo
12.5k1430
answered Jan 12 at 1:20
alexjoalexjo
12.5k1430
12.5k1430
add a comment |
add a comment |
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$begingroup$
Please also show the other method.
$endgroup$
– Peter
Jan 11 at 14:35
$begingroup$
It’s edited now, thanks!
$endgroup$
– quietkid
Jan 11 at 14:48
$begingroup$
@quietkid Since you know how to use MathJax I would recommend to write the equations in Mathjax. At the moment it is not clear which equations you´re talking about.
$endgroup$
– callculus
Jan 11 at 17:51