These are my banking details on an online game i play:
Account Type : Millionaire Double Platinum
Current Balance : 3,415,569 NP
Millionaire Double Platinum Interest Rate : 11% per year.
Yearly Interest : 375,712 NP
This interest rate means that you will gain 1,030 NP per day (it's rounded up)! You will have to claim this yourself by clicking the Collect Interest button below.
My question is how long will it take to get to $5,000,000 just with the daily interest going into the account, and what formula do i use to find this out?
y' = 0.11y, where y' is the amount you get per year, y is the amount you have, and t is time (in years)
dy/y = 0.11dt
ln(|y|) = 0.11t + C
y = C*e^(0.11t)
y(0) = 3,415,569
y(0) = C*e^0
C = 3,415,569
y = 3,415,569*e^(0.11t) --> This is the equation you're looking for
y = 5,000,000
5,000,000 = 3,415,569*e^(0.11t)
e^(0.11t) = 1.464
0.11t = 0.381
t = 3.464
If you don't know calculus, don't worry about the above. If you do, just ask and I'll explain all the steps.
Or are you saying that the interest rate is compounded daily? I'm having a little trouble understanding your wording.
Last edited by Ricky (2006-01-06 04:30:49)
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
yes its compounded daily. i tried to use the FV=P(1+r)^n equation, but i dont think its right for working it out
You were able to make 3.5 million neopoints. I am impressed. Did you gain it by the stockmarket.
thanks, i got most of it from playing games. i never did like the stock market much. i have no patience for holding onto the stocks for them long enough to make money lol.
I tried to figure it out myself and got 3.432 years using the equation:
n = log(A/P)/(q log[1+(i/q)])
where the annual rate of interest is i (as a fraction, that is 100i percent), the amount of the principal is P, the number of years is n, the number of times per year that the interest is compounded is q, and the amount after n years is A.
i=0.11, P=3427926, q=365, A=5000000
can someone please double check this for me because i havent done maths in years and i used the dodgy computer calculator so i may have made a mistake.
where P is initial money;
r - annual rate (as a decimal);
n - compounded (n times a year);
t - time(years);
A - amount after t years
answer 3.465009677 years
That's how it would be done mathematically, but because Neopets rounds the interest up every day, it would probably end up as being a bit less than that.
Why did the vector cross the road?
It wanted to be normal.