Mixing
What would the interest rate have to be to make the two shares to be equally valuable?
$begingroup$
Marco dies and leaves behind a perpetuity paying $1000/month. His wife is entitled to the payments for the first 20 years, and then payments go to Marco's favourite charity. Interest rates are 6% compounded monthly.
How much is Marco's wife share worth?
How much is the charity's share worth?
What would the interest rate have to be to make the two shares to be equally valuable?
For Marco's wife, since there are a finite set of payments with equal payments, the present value of Marco's wife's share would be an annuity.
$PV = 1000frac{1-v^{240}}{0.005} = 139,580.77 $
For the charity,
Since the charity will receive infinite payments after 20 years, it will be a perpetuity.
$PV(Charity) = 1000frac{1}{0.005}v^{20}=181,012.58$
I'm having trouble finding the interest rate that would make these two shares equal. Are the present values of Marco's wife and the charities correct?
finance actuarial-science
asked Jan 26 at 13:33
WadeWade
305311
$endgroup$
add a comment |
$begingroup$
Marco dies and leaves behind a perpetuity paying $1000/month. His wife is entitled to the payments for the first 20 years, and then payments go to Marco's favourite charity. Interest rates are 6% compounded monthly.
How much is Marco's wife share worth?
How much is the charity's share worth?
What would the interest rate have to be to make the two shares to be equally valuable?
For Marco's wife, since there are a finite set of payments with equal payments, the present value of Marco's wife's share would be an annuity.
$PV = 1000frac{1-v^{240}}{0.005} = 139,580.77 $
For the charity,
Since the charity will receive infinite payments after 20 years, it will be a perpetuity.
$PV(Charity) = 1000frac{1}{0.005}v^{20}=181,012.58$
I'm having trouble finding the interest rate that would make these two shares equal. Are the present values of Marco's wife and the charities correct?
finance actuarial-science
asked Jan 26 at 13:33
WadeWade
305311
$endgroup$
add a comment |
$begingroup$
Marco dies and leaves behind a perpetuity paying $1000/month. His wife is entitled to the payments for the first 20 years, and then payments go to Marco's favourite charity. Interest rates are 6% compounded monthly.
How much is Marco's wife share worth?
How much is the charity's share worth?
What would the interest rate have to be to make the two shares to be equally valuable?
For Marco's wife, since there are a finite set of payments with equal payments, the present value of Marco's wife's share would be an annuity.
$PV = 1000frac{1-v^{240}}{0.005} = 139,580.77 $
For the charity,
Since the charity will receive infinite payments after 20 years, it will be a perpetuity.
$PV(Charity) = 1000frac{1}{0.005}v^{20}=181,012.58$
I'm having trouble finding the interest rate that would make these two shares equal. Are the present values of Marco's wife and the charities correct?
finance actuarial-science
asked Jan 26 at 13:33
WadeWade
305311
$endgroup$
Marco dies and leaves behind a perpetuity paying $1000/month. His wife is entitled to the payments for the first 20 years, and then payments go to Marco's favourite charity. Interest rates are 6% compounded monthly.
How much is Marco's wife share worth?
How much is the charity's share worth?
What would the interest rate have to be to make the two shares to be equally valuable?
For Marco's wife, since there are a finite set of payments with equal payments, the present value of Marco's wife's share would be an annuity.
$PV = 1000frac{1-v^{240}}{0.005} = 139,580.77 $
For the charity,
Since the charity will receive infinite payments after 20 years, it will be a perpetuity.
$PV(Charity) = 1000frac{1}{0.005}v^{20}=181,012.58$
I'm having trouble finding the interest rate that would make these two shares equal. Are the present values of Marco's wife and the charities correct?
finance actuarial-science
finance actuarial-science
asked Jan 26 at 13:33
WadeWade
305311
asked Jan 26 at 13:33
WadeWade
305311
asked Jan 26 at 13:33
WadeWade
305311
asked Jan 26 at 13:33
WadeWade
305311
asked Jan 26 at 13:33
WadeWade
305311
305311
add a comment |
add a comment |
1 Answer
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$begingroup$
Your computation for the charity should have a $v^{240}$ rather than a $v^{20}$, meaning the value of the charity part is actually $$60,419.23$. (As a sanity check, the entire estate should be worth $frac{1000}{0.005}=$200,000$.)
If $r$ is the monthly interest rate, the entire perpetuity is worth $frac{1000}{r}$, while the charity portion of it is worth $frac{1000}{r} v^{240}$. You want the charity portion to be worth half as much as the whole thing, which means you need to find the interest rate where $v^{240}=frac{1}{2}$. Can you proceed from there?
answered Jan 26 at 15:15
MicahMicah
30.2k1364106
$endgroup$
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1 Answer
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$begingroup$
Your computation for the charity should have a $v^{240}$ rather than a $v^{20}$, meaning the value of the charity part is actually $$60,419.23$. (As a sanity check, the entire estate should be worth $frac{1000}{0.005}=$200,000$.)
If $r$ is the monthly interest rate, the entire perpetuity is worth $frac{1000}{r}$, while the charity portion of it is worth $frac{1000}{r} v^{240}$. You want the charity portion to be worth half as much as the whole thing, which means you need to find the interest rate where $v^{240}=frac{1}{2}$. Can you proceed from there?
answered Jan 26 at 15:15
MicahMicah
30.2k1364106
$endgroup$
add a comment |
$begingroup$
Your computation for the charity should have a $v^{240}$ rather than a $v^{20}$, meaning the value of the charity part is actually $$60,419.23$. (As a sanity check, the entire estate should be worth $frac{1000}{0.005}=$200,000$.)
If $r$ is the monthly interest rate, the entire perpetuity is worth $frac{1000}{r}$, while the charity portion of it is worth $frac{1000}{r} v^{240}$. You want the charity portion to be worth half as much as the whole thing, which means you need to find the interest rate where $v^{240}=frac{1}{2}$. Can you proceed from there?
answered Jan 26 at 15:15
MicahMicah
30.2k1364106
$endgroup$
add a comment |
$begingroup$
Your computation for the charity should have a $v^{240}$ rather than a $v^{20}$, meaning the value of the charity part is actually $$60,419.23$. (As a sanity check, the entire estate should be worth $frac{1000}{0.005}=$200,000$.)
If $r$ is the monthly interest rate, the entire perpetuity is worth $frac{1000}{r}$, while the charity portion of it is worth $frac{1000}{r} v^{240}$. You want the charity portion to be worth half as much as the whole thing, which means you need to find the interest rate where $v^{240}=frac{1}{2}$. Can you proceed from there?
answered Jan 26 at 15:15
MicahMicah
30.2k1364106
$endgroup$
Your computation for the charity should have a $v^{240}$ rather than a $v^{20}$, meaning the value of the charity part is actually $$60,419.23$. (As a sanity check, the entire estate should be worth $frac{1000}{0.005}=$200,000$.)
If $r$ is the monthly interest rate, the entire perpetuity is worth $frac{1000}{r}$, while the charity portion of it is worth $frac{1000}{r} v^{240}$. You want the charity portion to be worth half as much as the whole thing, which means you need to find the interest rate where $v^{240}=frac{1}{2}$. Can you proceed from there?
answered Jan 26 at 15:15
MicahMicah
30.2k1364106
answered Jan 26 at 15:15
MicahMicah
30.2k1364106
answered Jan 26 at 15:15
MicahMicah
30.2k1364106
answered Jan 26 at 15:15
MicahMicah
30.2k1364106
30.2k1364106
add a comment |
add a comment |
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