Unborncruel
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Hi,

Can someone please explain to me how to compound interest

ie the periodic rate/ monthly is 2%

So in a 1 year period that equates to 24% (12x2) however my study book says 2% compounded over 12 months is "26.8%"

Any help would be much appreciated

Thank u
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Towcestermaths
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(Original post by Unborncruel)
Hi,

Can someone please explain to me how to compound interest

ie the periodic rate/ monthly is 2%

So in a 1 year period that equates to 24% (12x2) however my study book says 2% compounded over 12 months is "26.8%"

Any help would be much appreciated

Thank u
Every month 2% interest is applied. Therefore at the end of each month there will be 102% of the money that was in the account at the start of the month (the original 100% plus the 2% interest). To calculate 102% of an amount you can multiply it by 1.02. Thus after the first month there will be 1.02 times the original amount in the account. At the end of the second month, you can multiply the amount that was in the account at the beginning of the second month by 1.02 again. Thus, in a year, the original amount will have been multiplied by 1.02 twelve times. So we find that at the end of the year there would be the original amount multiplied by 1.02^12. That is 1.268 which is 126.8%. Since you started with 100%, there is a total of 26.8% interest.
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Unborncruel
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(Original post by Towcestermaths)
Every month 2% interest is applied. Therefore at the end of each month there will be 102% of the money that was in the account at the start of the month (the original 100% plus the 2% interest). To calculate 102% of an amount you can multiply it by 1.02. Thus after the first month there will be 1.02 times the original amount in the account. At the end of the second month, you can multiply the amount that was in the account at the beginning of the second month by 1.02 again. Thus, in a year, the original amount will have been multiplied by 1.02 twelve times. So we find that at the end of the year there would be the original amount multiplied by 1.02^12. That is 1.268 which is 126.8%. Since you started with 100%, there is a total of 26.8% interest.

Thank u very very much for taking the time to explain that! I appreciate it

In relation to this- is it only possible to work out compounded interest with a calculator?

I've asked a friend who is quite good at maths and he said he very much doubts they would ask anyone to work out compounded interest with pen/ paper in an exam
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username3280668
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(Original post by Unborncruel)
Thank u very very much for taking the time to explain that! I appreciate it

In relation to this- is it only possible to work out compounded interest with a calculator?

I've asked a friend who is quite good at maths and he said he very much doubts they would ask anyone to work out compounded interest with pen/ paper in an exam
You can. Intial value x Multiplier ^How many times you want
Example: Guy starts £500, has 2% each year compound interest. How much money after 3 years.
500 x 1.02^3
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Towcestermaths
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(Original post by Unborncruel)
Thank u very very much for taking the time to explain that! I appreciate it

In relation to this- is it only possible to work out compounded interest with a calculator?

I've asked a friend who is quite good at maths and he said he very much doubts they would ask anyone to work out compounded interest with pen/ paper in an exam
He's right, unless it was something very simple like 10% or 5% over just two years say.
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Chinesetopteam
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(Original post by Throwaway740)
You can. Intial value x Multiplier ^How many times you want
Example: Guy starts £500, has 2% each year compound interest. How much money after 3 years.
500 x 1.02^3
Thank u very much- that's how I would do it on a calculator

Can u tell me if this is correct if I were to use pen/ paper

Using your sum

500 principle
2% Apr
3yr term

A technique I was taught would be

2+2+2= 6
2x2x2= 8
8/100 = 0.125

Hence 6.12%

500x6.12= 530.60

Is that okay? Sorry, I'm a complete noob at maths

But thank u both for the great advice
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Kyx
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(Original post by Unborncruel)
Hi,

Can someone please explain to me how to compound interest

ie the periodic rate/ monthly is 2%

So in a 1 year period that equates to 24% (12x2) however my study book says 2% compounded over 12 months is "26.8%"

Any help would be much appreciated

Thank u
1.02^12 = 1.268 = 26.8%


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Kyx
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(Original post by Chinesetopteam)
Thank u very much- that's how I would do it on a calculator

Can u tell me if this is correct if I were to use pen/ paper

Using your sum

500 principle
2% Apr
3yr term

A technique I was taught would be

2+2+2= 6
2x2x2= 8
8/100 = 0.125

Hence 6.12%

500x6.12= 530.60

Is that okay? Sorry, I'm a complete noob at maths

But thank u both for the great advice
500 x 1.02^3 = 530.60


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thekidwhogames
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(Original post by Unborncruel)
Hi,

Can someone please explain to me how to compound interest

ie the periodic rate/ monthly is 2%

So in a 1 year period that equates to 24% (12x2) however my study book says 2% compounded over 12 months is "26.8%"

Any help would be much appreciated

Thank u
You're thinking of simple interest. Compound interest is interest on your interest - therefore 2% and then 2% on that etc. So 1.02^12 = 1.268 --> percentage gain of 26.8%

Compound interest is a geometric progression which has the nth term a x r^n-1.

a = first term
r = common ratio

But in GCSE questions, they tell you to find the money AFTER years therefore the nth term wouldn't include the n-1 part; only a x r^n.
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