/biz/ - Business & Finance

yes.
the answer to your question is 1070

>>9467525
Yes to what? I asked two questions.

>>9467508
You can use your formula for continuous compounding interest:

A = Pe^rt

If you wanted to calculate discrete compounding interest, let's say calculating 5% monthly compounding interest for 2 years, you could do this:

A = P(1+ 0.05/12)^24 where the 12 represents the months and the 24 is the number of months in 2 years

>>9467508
Also, if you wanted to see what would happen to your investment if it grew by 7% each year, you don't even need to think in terms of formulas.

Just multiply your $1000 by 1.07 over and over again for the number of years you want to calculate.

Example, 5 years of 7% growth =
1000 * 1.07 * 1.07 * 1.07 * 1.07 * 1.07

>>9467851
Yes but I'm doing a summation. This only works out when you're looking in increments of exactly one year. If you're adding funds to an investment as the investment continually grows, it gets more complicated. For example, say a 1,000 dollar investment grows by 7% a year, but you're continually adding 1,000 dollars every month. Then what do you do to calculate the returns?

>>9467508
If i start with 1k and make 10% profit everyday for 100 days, how much did i earn?

>>9467938
Intuitively, my approach for that is to do that in Excel or Google Sheets. There may be a formula but I don't know one off the top of my head.

Why not just grab a free compounding interest calculator and plug in some numbers?

See pic related.

>>9467953
I'm trying to write a program in python that calculates which one of these options leaves you with the most money after 20 years, assuming you can get a 7% return on an investment. Normally I would think that paying off the loan as fast as possible is best, but since the interest rate is so low, I'm thinking it's actually better to delay paying it, assuming I can get a decent return on an investment.

>>9468054
?

>>9468054
Oh, wait, you said monthly.. sec.

>>9468054

>>9468282
Just tried this for 20 years... something doesn't seem right here. Hm.

>>9468054
I think this is right.

>>9468141

7% interest sounds realistic.

.. if you invest in practically riskless Argentine Bonds, Iranian Bonds or Turkish bonds, that is.

>>9468282
So what I'm doing is subtracting the payment amount from disposable income and assuming that I am investing the rest with an arbitrary percent return on investment.

>>9467508
Wow, you seldom see a thread with no OP image

>>9468391
You are subtracting 368.99 on both line 4 and on line 11.

Is this intentional? Why is it being done twice?

>>9468477
Because x-368.99 represents the disposable income. It's adding my theoretical disposable income every month to the amount invested. I suppose I could have just consolidated it into one variable.

So, assuming I did this correctly, the answer fits my intuition, which is that because the return on investment is larger than the interest rate, it's actually better to delay payment on the loan for as long as possible, assuming you invest all disposable income and get a constant 7% yield. How realistic is this scenario, though?

>>9468659
What kind of outputs does your program produce when you give it some inputs? Like, could you give me some sample inputs? From reading that code, it seems to me like your program would produce very large values for a time range like 20 years, but I could be wrong (I have not copied and tested your code)

And yeah, if your investments make more interest than the loss incurred by loan interest, it seems like it would make sense.

>>9468718
ya it produces absurdly large values, which makes me think there's a problem with the formula I chose, hence why I made this thread.

>>9468904
My code corresponds closely with what the calculators on free websites show, if you want to try it out (I'll paste below). Your for-loop is multiplying your total value by 2.178 for every iteration, which causes explosion. You must use discrete formula for your purpose, as below..

years = 20
disposableIncome = 4000
startAmount = 1000
interest = 0.07
monthlyAddition = 1000


# This is the discrete total. We compound by 0.07/12% every month.
for year in range(years*12):
startAmount = (startAmount + monthlyAddition) * (1 + interest/12)

print(startAmount)

>>9468965
It doesn't multiply by 2.178, it multiples by 2.178^(.06*(1/12)) (which is an incredibly small number). This is just the formula A=Pe^rt, which you said I could use. Looking at the numbers more closely, it actually looks realistic.

>>9469111
>>9468965
Nevermind, it's just wrong. I should probably be using simple interest rate as opposed to continuous. These numbers are way too high.

https://betterexplained.com/articles/a-visual-guide-to-simple-compound-and-continuous-interest-rates/

>>9468965
>>9469111
>>9469284
So upon researching it further, continuous interest rate is wrong because you're only supposed to use this when the amount of a thing changes how quickly it grows, such as for number of bacteria. It doesn't matter if you have 10,000 or 1,000 dollars invested in something, the rate of return is still the same.

>>9469111
I forgot that you're multiplying by a decimal, my bad.

>>9469347
The continuous interest rate just comes from the discrete interest rate when the limit of the intervals goes to infinity. So, if you compared the return on an investment compounded every 1 second by some super small percent vs the continuous compounding return, they would be very very close.

>>9469365
discrete interest formula*

>>9469365
Example..

Discrete (Compounded daily for 10 years)
A = 1000 * (1 + 0.07/365) ^ 3650 ≈ 2013.61755958

Continuous (Compounded every infinitely small time interval):
A = 1000 * e ^ (0.07 * 10) ≈ 2013.75270747

oh my god i just realized i was adding it twice with +=. No wonder the numbers were so large. derp