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Billy Bob, who is 22, won a prize of $5000 at McDonalds. He invests the money at
8% compounded quarterly for 43 years until he retires. When he retires, he then
reinvests the money at 7% compounded monthly and makes equal monthly
withdrawals for a further 25 years at which time the money would run out. How
much money would he get each month? Show all work
This is how I answered:
FV = R (1+i)^n = 5000(1+0.02)^172 where i=0.08/4 and n=43*4
FV = $150729.9473
Then:
PV= P [(1 + i)^n]- 1 / [1 + i]^n/i where i=0.07/12 and n = 24*12
$150729.9473 = P [(1 + 0.07/12)^24*12]-1 / [1+0.07/1]^24*12/0.07/12
P= $150729.9473 / 141.48690338
P = $1,065.33
However the answer should be 1,044.74 . I think I am doing something wrong with the interest. I know my answer is very close to the right answer but it is still incorrect.
functions discrete-mathematics finance
asked Jul 15 at 19:39
AneQo
284
add a comment |Â
up vote
1
down vote
favorite
Billy Bob, who is 22, won a prize of $5000 at McDonalds. He invests the money at
8% compounded quarterly for 43 years until he retires. When he retires, he then
reinvests the money at 7% compounded monthly and makes equal monthly
withdrawals for a further 25 years at which time the money would run out. How
much money would he get each month? Show all work
This is how I answered:
FV = R (1+i)^n = 5000(1+0.02)^172 where i=0.08/4 and n=43*4
FV = $150729.9473
Then:
PV= P [(1 + i)^n]- 1 / [1 + i]^n/i where i=0.07/12 and n = 24*12
$150729.9473 = P [(1 + 0.07/12)^24*12]-1 / [1+0.07/1]^24*12/0.07/12
P= $150729.9473 / 141.48690338
P = $1,065.33
However the answer should be 1,044.74 . I think I am doing something wrong with the interest. I know my answer is very close to the right answer but it is still incorrect.
functions discrete-mathematics finance
asked Jul 15 at 19:39
AneQo
284
In your first equation, shouldn't the interest be 0.08, and not 0.02 in $R(1+i) = 5000(1+0.08)^172$?
– amWhy
Jul 15 at 19:43
1
In the second part, shouldn't $n=25times 12$?
– lulu
Jul 15 at 19:45
1
Worth noting: your formulas are nearly unreadable. here is a good tutorial for formatting on this site.
– lulu
Jul 15 at 19:53
I think you have calculated $141.48690338$ as $left dfrac1-frac 1 [1+0.07/12]^25*120.07/12 right$ but this is not what I think you have written
– Henry
Jul 15 at 21:14
you'll have the result $1,044.74$ if $7%$ is the effective annual interest, so that the monthly interest is $i_m=1.07^1/12-1approx 0.57%$.
– alexjo
Jul 15 at 21:49
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Billy Bob, who is 22, won a prize of $5000 at McDonalds. He invests the money at
8% compounded quarterly for 43 years until he retires. When he retires, he then
reinvests the money at 7% compounded monthly and makes equal monthly
withdrawals for a further 25 years at which time the money would run out. How
much money would he get each month? Show all work
This is how I answered:
FV = R (1+i)^n = 5000(1+0.02)^172 where i=0.08/4 and n=43*4
FV = $150729.9473
Then:
PV= P [(1 + i)^n]- 1 / [1 + i]^n/i where i=0.07/12 and n = 24*12
$150729.9473 = P [(1 + 0.07/12)^24*12]-1 / [1+0.07/1]^24*12/0.07/12
P= $150729.9473 / 141.48690338
P = $1,065.33
However the answer should be 1,044.74 . I think I am doing something wrong with the interest. I know my answer is very close to the right answer but it is still incorrect.
functions discrete-mathematics finance
asked Jul 15 at 19:39
AneQo
284
Billy Bob, who is 22, won a prize of $5000 at McDonalds. He invests the money at
8% compounded quarterly for 43 years until he retires. When he retires, he then
reinvests the money at 7% compounded monthly and makes equal monthly
withdrawals for a further 25 years at which time the money would run out. How
much money would he get each month? Show all work
This is how I answered:
FV = R (1+i)^n = 5000(1+0.02)^172 where i=0.08/4 and n=43*4
FV = $150729.9473
Then:
PV= P [(1 + i)^n]- 1 / [1 + i]^n/i where i=0.07/12 and n = 24*12
$150729.9473 = P [(1 + 0.07/12)^24*12]-1 / [1+0.07/1]^24*12/0.07/12
P= $150729.9473 / 141.48690338
P = $1,065.33
However the answer should be 1,044.74 . I think I am doing something wrong with the interest. I know my answer is very close to the right answer but it is still incorrect.
functions discrete-mathematics finance
asked Jul 15 at 19:39
AneQo
284
asked Jul 15 at 19:39
AneQo
284
asked Jul 15 at 19:39
AneQo
284
asked Jul 15 at 19:39
AneQo
284
284
In your first equation, shouldn't the interest be 0.08, and not 0.02 in $R(1+i) = 5000(1+0.08)^172$?
– amWhy
Jul 15 at 19:43
1
In the second part, shouldn't $n=25times 12$?
– lulu
Jul 15 at 19:45
1
Worth noting: your formulas are nearly unreadable. here is a good tutorial for formatting on this site.
– lulu
Jul 15 at 19:53
I think you have calculated $141.48690338$ as $left dfrac1-frac 1 [1+0.07/12]^25*120.07/12 right$ but this is not what I think you have written
– Henry
Jul 15 at 21:14
you'll have the result $1,044.74$ if $7%$ is the effective annual interest, so that the monthly interest is $i_m=1.07^1/12-1approx 0.57%$.
– alexjo
Jul 15 at 21:49
add a comment |Â
In your first equation, shouldn't the interest be 0.08, and not 0.02 in $R(1+i) = 5000(1+0.08)^172$?
– amWhy
Jul 15 at 19:43
1
In the second part, shouldn't $n=25times 12$?
– lulu
Jul 15 at 19:45
1
Worth noting: your formulas are nearly unreadable. here is a good tutorial for formatting on this site.
– lulu
Jul 15 at 19:53
I think you have calculated $141.48690338$ as $left dfrac1-frac 1 [1+0.07/12]^25*120.07/12 right$ but this is not what I think you have written
– Henry
Jul 15 at 21:14
you'll have the result $1,044.74$ if $7%$ is the effective annual interest, so that the monthly interest is $i_m=1.07^1/12-1approx 0.57%$.
– alexjo
Jul 15 at 21:49
In your first equation, shouldn't the interest be 0.08, and not 0.02 in $R(1+i) = 5000(1+0.08)^172$?
– amWhy
Jul 15 at 19:43
In your first equation, shouldn't the interest be 0.08, and not 0.02 in $R(1+i) = 5000(1+0.08)^172$?
– amWhy
Jul 15 at 19:43
1
1
In the second part, shouldn't $n=25times 12$?
– lulu
Jul 15 at 19:45
In the second part, shouldn't $n=25times 12$?
– lulu
Jul 15 at 19:45
1
1
Worth noting: your formulas are nearly unreadable. here is a good tutorial for formatting on this site.
– lulu
Jul 15 at 19:53
Worth noting: your formulas are nearly unreadable. here is a good tutorial for formatting on this site.
– lulu
Jul 15 at 19:53
I think you have calculated $141.48690338$ as $left dfrac1-frac 1 [1+0.07/12]^25*120.07/12 right$ but this is not what I think you have written
– Henry
Jul 15 at 21:14
I think you have calculated $141.48690338$ as $left dfrac1-frac 1 [1+0.07/12]^25*120.07/12 right$ but this is not what I think you have written
– Henry
Jul 15 at 21:14
you'll have the result $1,044.74$ if $7%$ is the effective annual interest, so that the monthly interest is $i_m=1.07^1/12-1approx 0.57%$.
– alexjo
Jul 15 at 21:49
you'll have the result $1,044.74$ if $7%$ is the effective annual interest, so that the monthly interest is $i_m=1.07^1/12-1approx 0.57%$.
– alexjo
Jul 15 at 21:49
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
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If I´m right in total your equality was more or less
$$5000cdot 1.02^43cdot 4cdot (1+frac0.0712)^25cdot 12=Pcdot frac(1+0.07/12)^25cdot 12-1frac0.0712$$
As lulu has already mentioned, it has to be $25cdot 12$. But nevertheless I get the same result, $P=1065.33$. See here the result of the calculator w.a. And I agree with your calculation. I don´t see any mistake.
After testing other variations I´ve found out that they have used the $texttteffective interest rate$ (aka equivalent interest rate) for the $7%$.
To get the equivalent interest rate one has to solve the fowing equation
$left(1+fraci12 right)^12=1.07 Rightarrow i=(1.07^1/12-1)cdot 12=0.06784974465$
If you replace $0.07$ by the equivalent interest rate you´ll get the desired solution: calculator w.a. I think a little less number of digits is sufficient.
answered Jul 15 at 21:17
callculus
16.4k31427
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
If I´m right in total your equality was more or less
$$5000cdot 1.02^43cdot 4cdot (1+frac0.0712)^25cdot 12=Pcdot frac(1+0.07/12)^25cdot 12-1frac0.0712$$
As lulu has already mentioned, it has to be $25cdot 12$. But nevertheless I get the same result, $P=1065.33$. See here the result of the calculator w.a. And I agree with your calculation. I don´t see any mistake.
After testing other variations I´ve found out that they have used the $texttteffective interest rate$ (aka equivalent interest rate) for the $7%$.
To get the equivalent interest rate one has to solve the fowing equation
$left(1+fraci12 right)^12=1.07 Rightarrow i=(1.07^1/12-1)cdot 12=0.06784974465$
If you replace $0.07$ by the equivalent interest rate you´ll get the desired solution: calculator w.a. I think a little less number of digits is sufficient.
answered Jul 15 at 21:17
callculus
16.4k31427
add a comment |Â
up vote
1
down vote
accepted
If I´m right in total your equality was more or less
$$5000cdot 1.02^43cdot 4cdot (1+frac0.0712)^25cdot 12=Pcdot frac(1+0.07/12)^25cdot 12-1frac0.0712$$
As lulu has already mentioned, it has to be $25cdot 12$. But nevertheless I get the same result, $P=1065.33$. See here the result of the calculator w.a. And I agree with your calculation. I don´t see any mistake.
After testing other variations I´ve found out that they have used the $texttteffective interest rate$ (aka equivalent interest rate) for the $7%$.
To get the equivalent interest rate one has to solve the fowing equation
$left(1+fraci12 right)^12=1.07 Rightarrow i=(1.07^1/12-1)cdot 12=0.06784974465$
If you replace $0.07$ by the equivalent interest rate you´ll get the desired solution: calculator w.a. I think a little less number of digits is sufficient.
answered Jul 15 at 21:17
callculus
16.4k31427
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
If I´m right in total your equality was more or less
$$5000cdot 1.02^43cdot 4cdot (1+frac0.0712)^25cdot 12=Pcdot frac(1+0.07/12)^25cdot 12-1frac0.0712$$
As lulu has already mentioned, it has to be $25cdot 12$. But nevertheless I get the same result, $P=1065.33$. See here the result of the calculator w.a. And I agree with your calculation. I don´t see any mistake.
After testing other variations I´ve found out that they have used the $texttteffective interest rate$ (aka equivalent interest rate) for the $7%$.
To get the equivalent interest rate one has to solve the fowing equation
$left(1+fraci12 right)^12=1.07 Rightarrow i=(1.07^1/12-1)cdot 12=0.06784974465$
If you replace $0.07$ by the equivalent interest rate you´ll get the desired solution: calculator w.a. I think a little less number of digits is sufficient.
answered Jul 15 at 21:17
callculus
16.4k31427
If I´m right in total your equality was more or less
$$5000cdot 1.02^43cdot 4cdot (1+frac0.0712)^25cdot 12=Pcdot frac(1+0.07/12)^25cdot 12-1frac0.0712$$
As lulu has already mentioned, it has to be $25cdot 12$. But nevertheless I get the same result, $P=1065.33$. See here the result of the calculator w.a. And I agree with your calculation. I don´t see any mistake.
After testing other variations I´ve found out that they have used the $texttteffective interest rate$ (aka equivalent interest rate) for the $7%$.
To get the equivalent interest rate one has to solve the fowing equation
$left(1+fraci12 right)^12=1.07 Rightarrow i=(1.07^1/12-1)cdot 12=0.06784974465$
If you replace $0.07$ by the equivalent interest rate you´ll get the desired solution: calculator w.a. I think a little less number of digits is sufficient.
answered Jul 15 at 21:17
callculus
16.4k31427
edited Jul 15 at 21:58
answered Jul 15 at 21:17
callculus
16.4k31427
answered Jul 15 at 21:17
callculus
16.4k31427
answered Jul 15 at 21:17
callculus
16.4k31427
16.4k31427
add a comment |Â
add a comment |Â
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In your first equation, shouldn't the interest be 0.08, and not 0.02 in $R(1+i) = 5000(1+0.08)^172$?
– amWhy
Jul 15 at 19:43
1
In the second part, shouldn't $n=25times 12$?
– lulu
Jul 15 at 19:45
1
Worth noting: your formulas are nearly unreadable. here is a good tutorial for formatting on this site.
– lulu
Jul 15 at 19:53
I think you have calculated $141.48690338$ as $left dfrac1-frac 1 [1+0.07/12]^25*120.07/12 right$ but this is not what I think you have written
– Henry
Jul 15 at 21:14
you'll have the result $1,044.74$ if $7%$ is the effective annual interest, so that the monthly interest is $i_m=1.07^1/12-1approx 0.57%$.
– alexjo
Jul 15 at 21:49