How to calculate the value of a coin? [closed]

2

$begingroup$

I do not need a specific answer, but a global formula that solves this equation.

There is a coin that costs 100$ (or 5$ or $25 etc.) Each year, it steadily increases by 10% (or 1% or 4% etc.) How much did the coin cost 3 years ago?

X = price

Y = percent of increases

t = time

Thank you for help.

algebra-precalculus percentages geometric-progressions

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edited Jan 12 at 14:36

Martin Sleziak

44.8k10118272

asked Jan 12 at 14:32

Oleksandr OshekoOleksandr Osheko

132

$endgroup$

closed as off-topic by amWhy, Lord Shark the Unknown, Claude Leibovici, A. Pongrácz, Riccardo.Alestra Jan 18 at 9:20

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, Lord Shark the Unknown, Claude Leibovici, A. Pongrácz, Riccardo.Alestra

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Honestly, I am very bad at math and I don’t even have a clue where to start searching for this formula. If you know the answer then help, if not then the topic can be closed.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 15:00
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Try adding some of your work now... like the value$t$ years later, what you understood, or else this can be voted to be closed.
  $endgroup$
  – mm-crj
  Jan 12 at 16:00
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  This formula is needed for my website. I just replaced it with my variables and everything is calculated as needed. But thank you for worrying about my knowledge. The topic can be closed.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 16:13
  

  
  
  
  

add a comment | 

2

$begingroup$

I do not need a specific answer, but a global formula that solves this equation.

There is a coin that costs 100$ (or 5$ or $25 etc.) Each year, it steadily increases by 10% (or 1% or 4% etc.) How much did the coin cost 3 years ago?

X = price

Y = percent of increases

t = time

Thank you for help.

algebra-precalculus percentages geometric-progressions

share|cite|improve this question

edited Jan 12 at 14:36

Martin Sleziak

44.8k10118272

asked Jan 12 at 14:32

Oleksandr OshekoOleksandr Osheko

132

$endgroup$

closed as off-topic by amWhy, Lord Shark the Unknown, Claude Leibovici, A. Pongrácz, Riccardo.Alestra Jan 18 at 9:20

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, Lord Shark the Unknown, Claude Leibovici, A. Pongrácz, Riccardo.Alestra

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Honestly, I am very bad at math and I don’t even have a clue where to start searching for this formula. If you know the answer then help, if not then the topic can be closed.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 15:00
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Try adding some of your work now... like the value$t$ years later, what you understood, or else this can be voted to be closed.
  $endgroup$
  – mm-crj
  Jan 12 at 16:00
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  This formula is needed for my website. I just replaced it with my variables and everything is calculated as needed. But thank you for worrying about my knowledge. The topic can be closed.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 16:13
  

  
  
  
  

add a comment | 

2

2

2

1

$begingroup$

I do not need a specific answer, but a global formula that solves this equation.

There is a coin that costs 100$ (or 5$ or $25 etc.) Each year, it steadily increases by 10% (or 1% or 4% etc.) How much did the coin cost 3 years ago?

X = price

Y = percent of increases

t = time

Thank you for help.

algebra-precalculus percentages geometric-progressions

share|cite|improve this question

edited Jan 12 at 14:36

Martin Sleziak

44.8k10118272

asked Jan 12 at 14:32

Oleksandr OshekoOleksandr Osheko

132

$endgroup$

I do not need a specific answer, but a global formula that solves this equation.

There is a coin that costs 100$ (or 5$ or $25 etc.) Each year, it steadily increases by 10% (or 1% or 4% etc.) How much did the coin cost 3 years ago?

X = price

Y = percent of increases

t = time

Thank you for help.

algebra-precalculus percentages geometric-progressions

algebra-precalculus percentages geometric-progressions

share|cite|improve this question

edited Jan 12 at 14:36

Martin Sleziak

44.8k10118272

asked Jan 12 at 14:32

Oleksandr OshekoOleksandr Osheko

132

share|cite|improve this question

edited Jan 12 at 14:36

Martin Sleziak

44.8k10118272

asked Jan 12 at 14:32

Oleksandr OshekoOleksandr Osheko

132

share|cite|improve this question

share|cite|improve this question

edited Jan 12 at 14:36

Martin Sleziak

44.8k10118272

edited Jan 12 at 14:36

Martin Sleziak

44.8k10118272

edited Jan 12 at 14:36

Martin Sleziak

44.8k10118272

44.8k10118272

asked Jan 12 at 14:32

Oleksandr OshekoOleksandr Osheko

132

asked Jan 12 at 14:32

Oleksandr OshekoOleksandr Osheko

132

asked Jan 12 at 14:32

Oleksandr OshekoOleksandr Osheko

132

132

closed as off-topic by amWhy, Lord Shark the Unknown, Claude Leibovici, A. Pongrácz, Riccardo.Alestra Jan 18 at 9:20

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, Lord Shark the Unknown, Claude Leibovici, A. Pongrácz, Riccardo.Alestra

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by amWhy, Lord Shark the Unknown, Claude Leibovici, A. Pongrácz, Riccardo.Alestra Jan 18 at 9:20

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, Lord Shark the Unknown, Claude Leibovici, A. Pongrácz, Riccardo.Alestra

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Honestly, I am very bad at math and I don’t even have a clue where to start searching for this formula. If you know the answer then help, if not then the topic can be closed.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 15:00
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Try adding some of your work now... like the value$t$ years later, what you understood, or else this can be voted to be closed.
  $endgroup$
  – mm-crj
  Jan 12 at 16:00
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  This formula is needed for my website. I just replaced it with my variables and everything is calculated as needed. But thank you for worrying about my knowledge. The topic can be closed.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 16:13
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Honestly, I am very bad at math and I don’t even have a clue where to start searching for this formula. If you know the answer then help, if not then the topic can be closed.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 15:00
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Try adding some of your work now... like the value$t$ years later, what you understood, or else this can be voted to be closed.
  $endgroup$
  – mm-crj
  Jan 12 at 16:00
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  This formula is needed for my website. I just replaced it with my variables and everything is calculated as needed. But thank you for worrying about my knowledge. The topic can be closed.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 16:13
  

  
  
  
  

$begingroup$
Honestly, I am very bad at math and I don’t even have a clue where to start searching for this formula. If you know the answer then help, if not then the topic can be closed.
$endgroup$
– Oleksandr Osheko
Jan 12 at 15:00

$begingroup$
Honestly, I am very bad at math and I don’t even have a clue where to start searching for this formula. If you know the answer then help, if not then the topic can be closed.
$endgroup$
– Oleksandr Osheko
Jan 12 at 15:00

$begingroup$
Try adding some of your work now... like the value$t$ years later, what you understood, or else this can be voted to be closed.
$endgroup$
– mm-crj
Jan 12 at 16:00

$begingroup$
Try adding some of your work now... like the value$t$ years later, what you understood, or else this can be voted to be closed.
$endgroup$
– mm-crj
Jan 12 at 16:00

$begingroup$
This formula is needed for my website. I just replaced it with my variables and everything is calculated as needed. But thank you for worrying about my knowledge. The topic can be closed.
$endgroup$
– Oleksandr Osheko
Jan 12 at 16:13

$begingroup$
This formula is needed for my website. I just replaced it with my variables and everything is calculated as needed. But thank you for worrying about my knowledge. The topic can be closed.
$endgroup$
– Oleksandr Osheko
Jan 12 at 16:13

add a comment | 

2 Answers
2

active

oldest

votes

2

$begingroup$

Let's say the coin costs $x_0$$ at present. And its value increases monotonically by y% every year. Let the cost of the coin t years before was $x_{-t}$$.
Therefore,

begin{align}
&implies x_{-t} left(frac{y}{100}+1right)^t=x_0\
&implies x_{-t}= x_0left(frac{y}{100}+1right)^{-t}
end{align}

Here, $x_{-t}frac{y}{100}+x_{-t}$ is the increase in value $'t'$ years before.

share|cite|improve this answer

edited Jan 12 at 16:01

answered Jan 12 at 14:50

mm-crjmm-crj

425213

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your answer.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 15:23
  

  
  
  
  

add a comment | 

3

$begingroup$

See the table:
$$begin{array}{c|c|c|c|c|c}
t&-2&-1&0&1&\
hline
x_t&100(1+0.1)^{-2}&100(1+0.1)^{-1}&100&100(1+0.1)&\
hline
x_t&x_{-2}=x_0(1+0.1)^{-2}&x_{-1}=x_0(1+0.1)^{-1}&x_0&x_1=x_0(1+r)&
end{array}$$

share|cite|improve this answer

answered Jan 12 at 15:13

farruhotafarruhota

20.2k2738

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your answer.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 15:24
  

  
  
  
  

add a comment | 

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

2

$begingroup$

Let's say the coin costs $x_0$$ at present. And its value increases monotonically by y% every year. Let the cost of the coin t years before was $x_{-t}$$.
Therefore,

begin{align}
&implies x_{-t} left(frac{y}{100}+1right)^t=x_0\
&implies x_{-t}= x_0left(frac{y}{100}+1right)^{-t}
end{align}

Here, $x_{-t}frac{y}{100}+x_{-t}$ is the increase in value $'t'$ years before.

share|cite|improve this answer

edited Jan 12 at 16:01

answered Jan 12 at 14:50

mm-crjmm-crj

425213

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your answer.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 15:23
  

  
  
  
  

add a comment | 

2

$begingroup$

Let's say the coin costs $x_0$$ at present. And its value increases monotonically by y% every year. Let the cost of the coin t years before was $x_{-t}$$.
Therefore,

begin{align}
&implies x_{-t} left(frac{y}{100}+1right)^t=x_0\
&implies x_{-t}= x_0left(frac{y}{100}+1right)^{-t}
end{align}

Here, $x_{-t}frac{y}{100}+x_{-t}$ is the increase in value $'t'$ years before.

share|cite|improve this answer

edited Jan 12 at 16:01

answered Jan 12 at 14:50

mm-crjmm-crj

425213

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your answer.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 15:23
  

  
  
  
  

add a comment | 

2

2

2

$begingroup$

Let's say the coin costs $x_0$$ at present. And its value increases monotonically by y% every year. Let the cost of the coin t years before was $x_{-t}$$.
Therefore,

begin{align}
&implies x_{-t} left(frac{y}{100}+1right)^t=x_0\
&implies x_{-t}= x_0left(frac{y}{100}+1right)^{-t}
end{align}

Here, $x_{-t}frac{y}{100}+x_{-t}$ is the increase in value $'t'$ years before.

share|cite|improve this answer

edited Jan 12 at 16:01

answered Jan 12 at 14:50

mm-crjmm-crj

425213

$endgroup$

Let's say the coin costs $x_0$$ at present. And its value increases monotonically by y% every year. Let the cost of the coin t years before was $x_{-t}$$.
Therefore,

begin{align}
&implies x_{-t} left(frac{y}{100}+1right)^t=x_0\
&implies x_{-t}= x_0left(frac{y}{100}+1right)^{-t}
end{align}

Here, $x_{-t}frac{y}{100}+x_{-t}$ is the increase in value $'t'$ years before.

share|cite|improve this answer

edited Jan 12 at 16:01

answered Jan 12 at 14:50

mm-crjmm-crj

425213

share|cite|improve this answer

share|cite|improve this answer

edited Jan 12 at 16:01

edited Jan 12 at 16:01

edited Jan 12 at 16:01

answered Jan 12 at 14:50

mm-crjmm-crj

425213

answered Jan 12 at 14:50

mm-crjmm-crj

425213

answered Jan 12 at 14:50

mm-crjmm-crj

425213

425213

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your answer.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 15:23
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your answer.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 15:23
  

  
  
  
  

$begingroup$
Thank you for your answer.
$endgroup$
– Oleksandr Osheko
Jan 12 at 15:23

$begingroup$
Thank you for your answer.
$endgroup$
– Oleksandr Osheko
Jan 12 at 15:23

add a comment | 

3

$begingroup$

See the table:
$$begin{array}{c|c|c|c|c|c}
t&-2&-1&0&1&\
hline
x_t&100(1+0.1)^{-2}&100(1+0.1)^{-1}&100&100(1+0.1)&\
hline
x_t&x_{-2}=x_0(1+0.1)^{-2}&x_{-1}=x_0(1+0.1)^{-1}&x_0&x_1=x_0(1+r)&
end{array}$$

share|cite|improve this answer

answered Jan 12 at 15:13

farruhotafarruhota

20.2k2738

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your answer.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 15:24
  

  
  
  
  

add a comment | 

3

$begingroup$

See the table:
$$begin{array}{c|c|c|c|c|c}
t&-2&-1&0&1&\
hline
x_t&100(1+0.1)^{-2}&100(1+0.1)^{-1}&100&100(1+0.1)&\
hline
x_t&x_{-2}=x_0(1+0.1)^{-2}&x_{-1}=x_0(1+0.1)^{-1}&x_0&x_1=x_0(1+r)&
end{array}$$

share|cite|improve this answer

answered Jan 12 at 15:13

farruhotafarruhota

20.2k2738

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your answer.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 15:24
  

  
  
  
  

add a comment | 

3

3

3

$begingroup$

See the table:
$$begin{array}{c|c|c|c|c|c}
t&-2&-1&0&1&\
hline
x_t&100(1+0.1)^{-2}&100(1+0.1)^{-1}&100&100(1+0.1)&\
hline
x_t&x_{-2}=x_0(1+0.1)^{-2}&x_{-1}=x_0(1+0.1)^{-1}&x_0&x_1=x_0(1+r)&
end{array}$$

share|cite|improve this answer

answered Jan 12 at 15:13

farruhotafarruhota

20.2k2738

$endgroup$

See the table:
$$begin{array}{c|c|c|c|c|c}
t&-2&-1&0&1&\
hline
x_t&100(1+0.1)^{-2}&100(1+0.1)^{-1}&100&100(1+0.1)&\
hline
x_t&x_{-2}=x_0(1+0.1)^{-2}&x_{-1}=x_0(1+0.1)^{-1}&x_0&x_1=x_0(1+r)&
end{array}$$

share|cite|improve this answer

answered Jan 12 at 15:13

farruhotafarruhota

20.2k2738

share|cite|improve this answer

share|cite|improve this answer

answered Jan 12 at 15:13

farruhotafarruhota

20.2k2738

answered Jan 12 at 15:13

farruhotafarruhota

20.2k2738

answered Jan 12 at 15:13

farruhotafarruhota

20.2k2738

20.2k2738

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your answer.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 15:24
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your answer.
  $endgroup$
  – Oleksandr Osheko
  Jan 12 at 15:24
  

  
  
  
  

$begingroup$
Thank you for your answer.
$endgroup$
– Oleksandr Osheko
Jan 12 at 15:24

$begingroup$
Thank you for your answer.
$endgroup$
– Oleksandr Osheko
Jan 12 at 15:24

add a comment | 

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