Anyone good with math.
- Thread starter TheTunnel
- Start date
MachineLord
Supreme Member
- Aug 28, 2012
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rettaibi
Regular Member
- Jun 25, 2012
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I am not sure and I have no time to look it up but i think this.
If you are going to take 20% from the interest that you get every year, you can pretend like you get 80% from 20% interest.
you get 20% every year = 20/100 x 80 = 16.
I think this is the answer.
100 x 1,16^40 = 37872.11
A huge difference please anyone correct me if i am wrong.
If you are going to take 20% from the interest that you get every year, you can pretend like you get 80% from 20% interest.
you get 20% every year = 20/100 x 80 = 16.
I think this is the answer.
100 x 1,16^40 = 37872.11
A huge difference please anyone correct me if i am wrong.
Actually that is wrong, with that formula, 2nd year we would get 134.56 but actually it should be 139.20 when calculating manually.
Still can't get the equation, for those who didn't read the first post, the question is,
Suppose I invest $100 and get 20% interest per year.
And I withdraw 20% from the interest and reinvest the remaining 80% for making it compounding.
How would the equation be.
Normal compounding equation is A = p (1 + r)^y
Can anyone please help solve this problem ?
Thanks
Last edited:
pnvhq
Junior Member
- Jan 28, 2013
- 165
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TheTunnel, actually you're wrong. The problem with your manual calculation is you forgot to subtract out the 20% of interest you take out in the second year. If you did that, you would find that the numbers match up.
Yea, I was actually wrong, but you are wrong too.
it wouldn't be 139.2 (as I forgot to subtract the 20%), but it actually will be 131.36 and not 134.56
Because, 20% of 39.2 = 7.84,
now, 139.2 - 7.84 = 131.36
So, the principle would be 131.36
So, the formula of using 16 % is not correct.
If anyone can solve this, please comment and help me understand please.
Thanks
No, I did earn $39.20 in interest, we only calculate from the amount we receives as interest, so, the interest will keep increasing because the principle keeps increasing.
Simple.
$100 per year, 20% interest of which 80% reinvested and 20% withdrawn;
First year = $100 + $20 ($4 withdrawn, $16 reinvested) = $116 banked, $4 withdrawn
Second year = $116 + $23.2 ($4.64 withdrawn, $18.56 reinvested) = $134.56 banked, $8.64 withdrawn.
Lets call the first amount you put in 'a'.
a1 + (0.8*0.2*a1) = a2
a1 + 0.16*a1 = a2
1.16*a1 = a2
a2 + 0.16*a2 = a3 = 1.16(a2) = 1.16*1.16(a2) therefore 1.16^YEARS(a1) = total banked amount after YEARS.
For the amount withdrawn after a given number of years:
a1 * 0.2 * 0.2 = b1 therefore a1*0.04 = b1
(a1 * 1.16 * 0.04) + b1 = (a2*0.04) + b1= b2
b1 = a1*0.04
b2 = (a1*1.16*0.04) + (a1*0.04)
Therefore bYEAR = ∑ (100*(1.16^a)*0.04) from a=0 to YEAR
Can't be bothered to find the expanded form right now, but that's the basics.
EG,
Total amount earned over 2 years = $143.2 with $100 initial investment:
Wolfram Alpha Calculation
Total amount earned over 40 years = $47.315 with $100 initial investment:
Wolfram Alpha Calculation
So yeah, rettaibi, you were wrong
$100 per year, 20% interest of which 80% reinvested and 20% withdrawn;
First year = $100 + $20 ($4 withdrawn, $16 reinvested) = $116 banked, $4 withdrawn
Second year = $116 + $23.2 ($4.64 withdrawn, $18.56 reinvested) = $134.56 banked, $8.64 withdrawn.
Lets call the first amount you put in 'a'.
a1 + (0.8*0.2*a1) = a2
a1 + 0.16*a1 = a2
1.16*a1 = a2
a2 + 0.16*a2 = a3 = 1.16(a2) = 1.16*1.16(a2) therefore 1.16^YEARS(a1) = total banked amount after YEARS.
For the amount withdrawn after a given number of years:
a1 * 0.2 * 0.2 = b1 therefore a1*0.04 = b1
(a1 * 1.16 * 0.04) + b1 = (a2*0.04) + b1= b2
b1 = a1*0.04
b2 = (a1*1.16*0.04) + (a1*0.04)
Therefore bYEAR = ∑ (100*(1.16^a)*0.04) from a=0 to YEAR
Can't be bothered to find the expanded form right now, but that's the basics.
EG,
Total amount earned over 2 years = $143.2 with $100 initial investment:
Wolfram Alpha Calculation
Total amount earned over 40 years = $47.315 with $100 initial investment:
Wolfram Alpha Calculation
So yeah, rettaibi, you were wrong
Last edited:
Thanks, but I was bad in math so don't understand it much.
I think rettaibi told correct in simple format, if I withdraw 20% from interest, than 20% of 20% would be 4%, so 20% minus 4% would be 16% which is actually correct.
Haha sorry I got a little bit carried away there...
Depends if you're looking at the total amount of money you have, or the amount of money you have in your bank.
The simple calculation will work for the amount of money in your bank, but it completely forgets the amount of money you've taken out every year too! It doesn't make much of a difference to begin with, but because it's a 'power expression', that quickly adds up!
(Nearly $10k difference after 40 years!)
Furious George
Supreme Member
- Dec 13, 2012
- 1,438
- 2,188
you just spammed this forum with your math homework? Seriously dude?
Wrong section yes, but it's maths relating to compound interest, important for many working in internet marketing - my answer may be helpful to others too
Hey, I have another question I think you can help me solve.
Suppose I get 20% per year and withdraw 20% of the 20%, I would need to use 16% interest instead right, so I can now calculate the amount I will have.But, what if I want to know the total amount I have withdrawn, you know how to calculate that.I tried using 4% instead in the compound calculator but it's very small figure and I don't think it's the correct answer.
Thanks
switch_2012
Power Member
- Feb 28, 2010
- 504
- 229
'm working on my flux capacitor if i get a chance will look at it..
Covered that in my original answer, but i'll show the calculation again here
∑ (INITIAL INVESTMENT*(1.16^a)*0.04) from a=0 to (YEARS-1)
I explained how I derived that expression in my post before, but it's quite complicated maths so don't worry if you can't follow it yet (just easier than simple degree level)
EG,
$100 initial investment, after 1 year total withdrawn =
Wolfram Alpha Calculation
$100 initial investment, after 2 year total withdrawn =
Wolfram Alpha Calculation
$100 initial investment, after 40 year total withdrawn =
Wolfram Alpha Calculation
Covered that in my original answer, but i'll show the calculation again here
∑ (INITIAL INVESTMENT*(1.16^a)*0.04) from a=0 to (YEARS-1)
I explained how I derived that expression in my post before, but it's quite complicated maths so don't worry if you can't follow it yet (just easier than simple degree level)
EG,
Thanks alot, solved it perfectly.