Daily Increase of Interest?
Sun Aug 06, 2006 6:05 pm
Hi guys
I remember a few months ago someone asked this question, and I used the "search" function to look up that old post, but I got 171 PAGES of posts returned... I tried typing more words to narrow down my search, but still.. anyhow I want you to know I at least tried!
Anyhow, the question is, how many NP would you have to have in the bank, so that whenever you collected your interest, the next day you would get more interest?
Assuming that you level up your interest level as you go... for instance, from 1,000,000 to 1,999,999 you have millionaire platinum, from 2,000,000 - 4,999,999 you have millionaire double platinum... and you don't go up to 5 mil, get mega-plat, then reduce your NP down to 1,250,000. Get it?
Thank you!!
I remember a few months ago someone asked this question, and I used the "search" function to look up that old post, but I got 171 PAGES of posts returned... I tried typing more words to narrow down my search, but still.. anyhow I want you to know I at least tried!
Anyhow, the question is, how many NP would you have to have in the bank, so that whenever you collected your interest, the next day you would get more interest?
Assuming that you level up your interest level as you go... for instance, from 1,000,000 to 1,999,999 you have millionaire platinum, from 2,000,000 - 4,999,999 you have millionaire double platinum... and you don't go up to 5 mil, get mega-plat, then reduce your NP down to 1,250,000. Get it?
Thank you!!
Sun Aug 06, 2006 7:53 pm
I only have millionaire-mega-platinum, so I went with that interest rate (11.5%/year). To make 1 NP in interest per day, you would need 3174NP (365/0.115). So if your interest is 3174 on day 1 and you didn't add any other NP to your account, your interest the second day would be 3175. The third, day you would get 3176, until you reached enough for it to go up by 2 NP/day. In order for a MMP account to generate 3174NP in interest, you would need 10,074,000NP in it (i.e., an ultimate riches account). The formula is 3174=x times 0.115/365; solving for x gives you the 10 million number. The actual number is a little lower. If you know the interest rate, just sub it in for 0.115 in the above formulae and you'll have it.
Mon Aug 07, 2006 1:59 pm
Whew, that is confusing. Glad you understand it!
Thank you for helping me out!
Mon Aug 07, 2006 6:25 pm
Sorry it was confusing. Here's where the numbers come from:
The annual interest rate is 0.115 (11.5%).
Since this is given out daily, you need to divide that rate by the number of days in a year to get the daily interest rate (0.115/365).
The formula for the amount of interest you receive each day is:
y = r * x (where y = amount you receive, r = daily interest rate calculated above, and x = amount in the bank).
If you want to find out how much interest you'll receive tomorrow knowing that you have x NP in the bank today, you can modify the above formula:
y(tom) = r * (x + y(tod)) where y(tom) stands for tomorrow's interest and y(tod) stands for today's interest. That's because the Neopian bank compounds daily. A little bit of algebra tells you that
y(tom) = (r * x) + (r * y(tod)).
But we know that r * x = y(tod), so the formula becomes:
y(tom) = y(tod) + (r * y(tod)).
In order for y(tom) to be greater than y(tod) , we need r * y(tod) to be greater than or equal to 1. So we'll just set it equal to 1 to find the minimum:
1 = r * y(tod)
Solving for y(tod) gives us y(tod) = 1/r. Subbing in the formula for r, we get y(tod) = 1/(0.115/365) = 365/0.115.
Now we know how much interest we want today. So we put that into our original formula:
y(tod) = r * x. Solving for x, we get x = y(tod)/r. We could reduce this equation further by subbing in the above equation for y(tod). Thus,
x = (1/r)/r = 1/(r^2)=365^2/0.115^2.
I hope this was a little more clear. Because the Neopian bank always rounds up to a whole NP amount, you might start getting almost daily interest increases well before the amount you calculate using the correct interest rate for your account. But it won't be truly daily until you reach the amount in the formula.
The annual interest rate is 0.115 (11.5%).
Since this is given out daily, you need to divide that rate by the number of days in a year to get the daily interest rate (0.115/365).
The formula for the amount of interest you receive each day is:
y = r * x (where y = amount you receive, r = daily interest rate calculated above, and x = amount in the bank).
If you want to find out how much interest you'll receive tomorrow knowing that you have x NP in the bank today, you can modify the above formula:
y(tom) = r * (x + y(tod)) where y(tom) stands for tomorrow's interest and y(tod) stands for today's interest. That's because the Neopian bank compounds daily. A little bit of algebra tells you that
y(tom) = (r * x) + (r * y(tod)).
But we know that r * x = y(tod), so the formula becomes:
y(tom) = y(tod) + (r * y(tod)).
In order for y(tom) to be greater than y(tod) , we need r * y(tod) to be greater than or equal to 1. So we'll just set it equal to 1 to find the minimum:
1 = r * y(tod)
Solving for y(tod) gives us y(tod) = 1/r. Subbing in the formula for r, we get y(tod) = 1/(0.115/365) = 365/0.115.
Now we know how much interest we want today. So we put that into our original formula:
y(tod) = r * x. Solving for x, we get x = y(tod)/r. We could reduce this equation further by subbing in the above equation for y(tod). Thus,
x = (1/r)/r = 1/(r^2)=365^2/0.115^2.
I hope this was a little more clear. Because the Neopian bank always rounds up to a whole NP amount, you might start getting almost daily interest increases well before the amount you calculate using the correct interest rate for your account. But it won't be truly daily until you reach the amount in the formula.
Thu Aug 10, 2006 12:32 am
Yep - thank god to rounding. What I plan to do actually is just make a lot of np so I can collect like... 50,000 interest from the bank every day