Feeling dumb, compound interest headache
Discussion
Ok, so the formula itself isn't a problem. I have all the figures I need and the rest is easy to understand. What I'm struggling with appears to be so basic that it isn't explained anywhere 
So here is a ripped explanation just quickly:
The formula for annual compound interest is A = P (1 + r/n) ^ nt
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
Why the 1 +
Please god why the 1 +
I assume it's saying to use it once in the formula but why would it need to be there at all?
I'll add, I was awful with all things mathematics at school so my foundation is terrible.
Please help an idiot
So here is a ripped explanation just quickly:
The formula for annual compound interest is A = P (1 + r/n) ^ nt
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
Why the 1 +
Please god why the 1 +
I assume it's saying to use it once in the formula but why would it need to be there at all?
I'll add, I was awful with all things mathematics at school so my foundation is terrible.
Please help an idiot
Go on I'll try.
It's because it is multiplied by the P, the principal investment amount.
r/n gives the fraction of the interest, (1+r/n) adds the fraction of the interst and keeps the original P too.
If that makes sense.
So if r=1.5% and n=12 months
r/n = 0.125
if P was £100 then P x r/n = £12.5
but P x (1+r/n) = £112.5 - the interest is essentially added to P ready for the next calculation.
Edit for completeness the ^nt term does the following.
It takes the number of compounds in the year and multiplies it by the number of years - so a count of how many times over the term of the loan/investment interest with be calculated according to P x (1+r/n).
By raising P x (1+r/n) (the interest added to P at each compound) to the power of nt it essentially multiplies P x (1+r/n) by itself for each compound in the loan/investment term.
HTH
It's because it is multiplied by the P, the principal investment amount.
r/n gives the fraction of the interest, (1+r/n) adds the fraction of the interst and keeps the original P too.
If that makes sense.
So if r=1.5% and n=12 months
r/n = 0.125
if P was £100 then P x r/n = £12.5
but P x (1+r/n) = £112.5 - the interest is essentially added to P ready for the next calculation.
Edit for completeness the ^nt term does the following.
It takes the number of compounds in the year and multiplies it by the number of years - so a count of how many times over the term of the loan/investment interest with be calculated according to P x (1+r/n).
By raising P x (1+r/n) (the interest added to P at each compound) to the power of nt it essentially multiplies P x (1+r/n) by itself for each compound in the loan/investment term.
HTH
Edited by TheExcession on Friday 2nd October 12:08
TheExcession said:
Go on I'll try.
It's because it is multiplied by the P, the principal investment amount.
r/n gives the fraction of the interest, (1+r/n) adds the fraction of the interst and keeps the original P too.
If that makes sense.
That does make sense, thank you! If I had a 2 + I would be effectively doubling my initial amount by that logicIt's because it is multiplied by the P, the principal investment amount.
r/n gives the fraction of the interest, (1+r/n) adds the fraction of the interst and keeps the original P too.
If that makes sense.
Aphex said:
TheExcession said:
Go on I'll try.
It's because it is multiplied by the P, the principal investment amount.
r/n gives the fraction of the interest, (1+r/n) adds the fraction of the interst and keeps the original P too.
If that makes sense.
That does make sense, thank you! If I had a 2 + I would be effectively doubling my initial amount by that logicIt's because it is multiplied by the P, the principal investment amount.
r/n gives the fraction of the interest, (1+r/n) adds the fraction of the interst and keeps the original P too.
If that makes sense.
The 1 has to remain as a 1 - it's a constant part of the formula - the way it works - you can only change values associated with the 'letters' in the equation.
If you want to double your initial amount then that change occurs in the P value. e.g. £100 or £200.
No I wouldn't do that. I suppose my frustration comes in that it uses a number where it would make more sense to me for that to have it's own term rather than using numbers.
Especially when trying to pull it apart an change it to see the outcome when 'its the way it works' is the only explanation there is
Especially when trying to pull it apart an change it to see the outcome when 'its the way it works' is the only explanation there is
Aphex said:
I suppose my frustration comes in that it uses a number where it would make more sense to me for that to have it's own term rather than using numbers.
But the '1' is its own term - it means 1 of P plus r/n of P - you could write the whole equation out in log hand to show(Px1) + (Pxr/n)
which is (P) + P x r / n
i.e. we are adding the full part of P to the r/n part of P - which is a smaller fraction.
Just think of the '1' as being anything outside of the brackets - in this case P.
In this case P(1+r/n) == ( (Px1) + (P x r / n) )
The notation just gets rid of a lot of the P
Everything out side the brackets gets multiplied by everything inside the brackets and as you can see we end up with less Ps - but actually more P!
thanks for bearing with me there, appreciate the help 
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