a formula for calculating value of interest bearing account to which I make monthly deposits
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I have two sons, ages 6 and 11, for whom I deposit 50 dollars each into separate education accounts. I think it would be more fair to give my older son a larger amount monthly so that by the time they each turn 18, I will have invested the same amount of money into their accounts. I have noodled around with amortization formulas but I'm not a good enough mathematician to produce a convincing answer to my problem. Basically, I want x dollars invested in an interest bearing account monthly for the next 84 months to equal $(100-x) invested in a similar account for the next 144 months. What is a good formula for figuring this out?
summation logarithms finance
asked Sep 11 at 3:19
Collin Waltner
91
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I have two sons, ages 6 and 11, for whom I deposit 50 dollars each into separate education accounts. I think it would be more fair to give my older son a larger amount monthly so that by the time they each turn 18, I will have invested the same amount of money into their accounts. I have noodled around with amortization formulas but I'm not a good enough mathematician to produce a convincing answer to my problem. Basically, I want x dollars invested in an interest bearing account monthly for the next 84 months to equal $(100-x) invested in a similar account for the next 144 months. What is a good formula for figuring this out?
summation logarithms finance
asked Sep 11 at 3:19
Collin Waltner
91
Do you know what is the interest rate?
– Mohammad Riazi-Kermani
Sep 11 at 3:28
It accrues roughly 8% annually, but I do not actually know how it is compounded
– Collin Waltner
Sep 11 at 17:30
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I have two sons, ages 6 and 11, for whom I deposit 50 dollars each into separate education accounts. I think it would be more fair to give my older son a larger amount monthly so that by the time they each turn 18, I will have invested the same amount of money into their accounts. I have noodled around with amortization formulas but I'm not a good enough mathematician to produce a convincing answer to my problem. Basically, I want x dollars invested in an interest bearing account monthly for the next 84 months to equal $(100-x) invested in a similar account for the next 144 months. What is a good formula for figuring this out?
summation logarithms finance
asked Sep 11 at 3:19
Collin Waltner
91
I have two sons, ages 6 and 11, for whom I deposit 50 dollars each into separate education accounts. I think it would be more fair to give my older son a larger amount monthly so that by the time they each turn 18, I will have invested the same amount of money into their accounts. I have noodled around with amortization formulas but I'm not a good enough mathematician to produce a convincing answer to my problem. Basically, I want x dollars invested in an interest bearing account monthly for the next 84 months to equal $(100-x) invested in a similar account for the next 144 months. What is a good formula for figuring this out?
summation logarithms finance
summation logarithms finance
asked Sep 11 at 3:19
Collin Waltner
91
asked Sep 11 at 3:19
Collin Waltner
91
asked Sep 11 at 3:19
Collin Waltner
91
asked Sep 11 at 3:19
Collin Waltner
91
asked Sep 11 at 3:19
Collin Waltner
91
91
Do you know what is the interest rate?
– Mohammad Riazi-Kermani
Sep 11 at 3:28
It accrues roughly 8% annually, but I do not actually know how it is compounded
– Collin Waltner
Sep 11 at 17:30
add a comment |
Do you know what is the interest rate?
– Mohammad Riazi-Kermani
Sep 11 at 3:28
It accrues roughly 8% annually, but I do not actually know how it is compounded
– Collin Waltner
Sep 11 at 17:30
Do you know what is the interest rate?
– Mohammad Riazi-Kermani
Sep 11 at 3:28
Do you know what is the interest rate?
– Mohammad Riazi-Kermani
Sep 11 at 3:28
It accrues roughly 8% annually, but I do not actually know how it is compounded
– Collin Waltner
Sep 11 at 17:30
It accrues roughly 8% annually, but I do not actually know how it is compounded
– Collin Waltner
Sep 11 at 17:30
add a comment |
1 Answer
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2
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Yes, there is a mathematical answer to this. If you invest $x$ dollars per month at the beginning of the month at $i$ per month compound interest for $n$ months, one month after the last deposit the last one will be worth $x(1+i)$ and the first will be worth $x(1+i)^n$. This is a geometric series with sum $x(1+i)frac (1+i)^n-1i$ so your equation is
$$x(1+i)frac (1+i)^84-1i=(100-x)(1+i)frac (1+i)^144-1i$$
Fairness is not a mathematical term. This calculation will result in each son having the same number of then-year dollars one month after your last deposit. Do you want to consider the effect of inflation during the five years? Your younger son will presumably face higher prices in the time he is in college. How much do you think the inflation will be? In the US for the past few decades the cost of college has risen faster than inflation. Maybe this last belongs on personal finance.se
answered Sep 11 at 3:48
Ross Millikan
286k23195363
Thank you so much for a very understandable answer!
– Collin Waltner
Sep 11 at 17:23
And you are correct: Fairness is a poor mathematical term and a nearly impossible financial consideration. In order to be "fair", I should probably start by depositing considerably more than $50 into their respective accounts!
– Collin Waltner
Sep 11 at 17:25
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
Yes, there is a mathematical answer to this. If you invest $x$ dollars per month at the beginning of the month at $i$ per month compound interest for $n$ months, one month after the last deposit the last one will be worth $x(1+i)$ and the first will be worth $x(1+i)^n$. This is a geometric series with sum $x(1+i)frac (1+i)^n-1i$ so your equation is
$$x(1+i)frac (1+i)^84-1i=(100-x)(1+i)frac (1+i)^144-1i$$
Fairness is not a mathematical term. This calculation will result in each son having the same number of then-year dollars one month after your last deposit. Do you want to consider the effect of inflation during the five years? Your younger son will presumably face higher prices in the time he is in college. How much do you think the inflation will be? In the US for the past few decades the cost of college has risen faster than inflation. Maybe this last belongs on personal finance.se
answered Sep 11 at 3:48
Ross Millikan
286k23195363
Thank you so much for a very understandable answer!
– Collin Waltner
Sep 11 at 17:23
And you are correct: Fairness is a poor mathematical term and a nearly impossible financial consideration. In order to be "fair", I should probably start by depositing considerably more than $50 into their respective accounts!
– Collin Waltner
Sep 11 at 17:25
add a comment |
up vote
2
down vote
Yes, there is a mathematical answer to this. If you invest $x$ dollars per month at the beginning of the month at $i$ per month compound interest for $n$ months, one month after the last deposit the last one will be worth $x(1+i)$ and the first will be worth $x(1+i)^n$. This is a geometric series with sum $x(1+i)frac (1+i)^n-1i$ so your equation is
$$x(1+i)frac (1+i)^84-1i=(100-x)(1+i)frac (1+i)^144-1i$$
Fairness is not a mathematical term. This calculation will result in each son having the same number of then-year dollars one month after your last deposit. Do you want to consider the effect of inflation during the five years? Your younger son will presumably face higher prices in the time he is in college. How much do you think the inflation will be? In the US for the past few decades the cost of college has risen faster than inflation. Maybe this last belongs on personal finance.se
answered Sep 11 at 3:48
Ross Millikan
286k23195363
Thank you so much for a very understandable answer!
– Collin Waltner
Sep 11 at 17:23
And you are correct: Fairness is a poor mathematical term and a nearly impossible financial consideration. In order to be "fair", I should probably start by depositing considerably more than $50 into their respective accounts!
– Collin Waltner
Sep 11 at 17:25
add a comment |
up vote
2
down vote
up vote
2
down vote
Yes, there is a mathematical answer to this. If you invest $x$ dollars per month at the beginning of the month at $i$ per month compound interest for $n$ months, one month after the last deposit the last one will be worth $x(1+i)$ and the first will be worth $x(1+i)^n$. This is a geometric series with sum $x(1+i)frac (1+i)^n-1i$ so your equation is
$$x(1+i)frac (1+i)^84-1i=(100-x)(1+i)frac (1+i)^144-1i$$
Fairness is not a mathematical term. This calculation will result in each son having the same number of then-year dollars one month after your last deposit. Do you want to consider the effect of inflation during the five years? Your younger son will presumably face higher prices in the time he is in college. How much do you think the inflation will be? In the US for the past few decades the cost of college has risen faster than inflation. Maybe this last belongs on personal finance.se
answered Sep 11 at 3:48
Ross Millikan
286k23195363
Yes, there is a mathematical answer to this. If you invest $x$ dollars per month at the beginning of the month at $i$ per month compound interest for $n$ months, one month after the last deposit the last one will be worth $x(1+i)$ and the first will be worth $x(1+i)^n$. This is a geometric series with sum $x(1+i)frac (1+i)^n-1i$ so your equation is
$$x(1+i)frac (1+i)^84-1i=(100-x)(1+i)frac (1+i)^144-1i$$
Fairness is not a mathematical term. This calculation will result in each son having the same number of then-year dollars one month after your last deposit. Do you want to consider the effect of inflation during the five years? Your younger son will presumably face higher prices in the time he is in college. How much do you think the inflation will be? In the US for the past few decades the cost of college has risen faster than inflation. Maybe this last belongs on personal finance.se
answered Sep 11 at 3:48
Ross Millikan
286k23195363
answered Sep 11 at 3:48
Ross Millikan
286k23195363
answered Sep 11 at 3:48
Ross Millikan
286k23195363
answered Sep 11 at 3:48
Ross Millikan
286k23195363
286k23195363
Thank you so much for a very understandable answer!
– Collin Waltner
Sep 11 at 17:23
And you are correct: Fairness is a poor mathematical term and a nearly impossible financial consideration. In order to be "fair", I should probably start by depositing considerably more than $50 into their respective accounts!
– Collin Waltner
Sep 11 at 17:25
add a comment |
Thank you so much for a very understandable answer!
– Collin Waltner
Sep 11 at 17:23
And you are correct: Fairness is a poor mathematical term and a nearly impossible financial consideration. In order to be "fair", I should probably start by depositing considerably more than $50 into their respective accounts!
– Collin Waltner
Sep 11 at 17:25
Thank you so much for a very understandable answer!
– Collin Waltner
Sep 11 at 17:23
Thank you so much for a very understandable answer!
– Collin Waltner
Sep 11 at 17:23
And you are correct: Fairness is a poor mathematical term and a nearly impossible financial consideration. In order to be "fair", I should probably start by depositing considerably more than $50 into their respective accounts!
– Collin Waltner
Sep 11 at 17:25
And you are correct: Fairness is a poor mathematical term and a nearly impossible financial consideration. In order to be "fair", I should probably start by depositing considerably more than $50 into their respective accounts!
– Collin Waltner
Sep 11 at 17:25
add a comment |
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Do you know what is the interest rate?
– Mohammad Riazi-Kermani
Sep 11 at 3:28
It accrues roughly 8% annually, but I do not actually know how it is compounded
– Collin Waltner
Sep 11 at 17:30