Original amount is $50,000.  Interest rate is a constant 10% per year.  What is my total at the end of 30 years?

What forumla do I use to figure this out?
Thanks

Is this continuously compounded interest (usually is in real life situations), or is interest tacked on only once a year? If it's the latter, you should easily be able to derive the appropriate formula.

Let's see if I remember correctly...

Amount = Principle*(1 + Rate/c)^(N*c)

Where c is the number of times it is compounded per year, and N is the number of years.  In your case, c == 1, so

A = Principle * (1 + Rate)^Years

[quote author=RageOfOrder @ F150Online.com]is this compounding interest or not?

basically the formula is:
P(1+ r/n)^nt

where
P = principle amount
r = interest rate (in percent)
n = number of payments per year
t = number of years

so we have 50,000 (1 + (.1/1)) ^(1*30)
which = $872,470.11
That is correct IF it is compound interest.

If not, then it is simply (10% of 50,000) * 30 and then add that to the original 50,000
Leaving you with $200,000.00[/quote]

Interest is compounded in & interest builds off previously made interest (I don't recall specific terms that we used in algebra, I haven't done stuff like this in 6 years.)

This is real world, too, btw.

Thanks for the help.  Math is annoying.

It will be continuously compounded interest.  This is something you should be able to derive.   

http://www.moneychimp.com/articles/finworks/continuous_compounding.htm

10% interest rate?! WHAT BANK?!

After 0 years you have 50,000
After 1 year you have 50,000 * 1.1
After 2 years you have (50,000 * 1.1) * 1.1 = 50,000 * 1.1^2
After 3 years you have (50,000 * 1.1^2) * 1.1 = 50,000 * 1.1^3
...
After n years you have 50,000 * 1.1^n

50,000 * (1.1^30) == 872,470.11

[quote author=Topaz link=topic=14397.msg147393#msg147393 date=1141232492]
10% interest rate?! WHAT BANK?!
[/quote]It is invest ments.  That was the projected average annual interest return over 30 years.  There were some years where loss was 20%.

Thanks Yoni!

Ugh no.  That is not the answer you want.  Continuously compounded interest.

Think about the number 'e', or click that link I posted.

[quote author=Rule link=topic=14397.msg147412#msg147412 date=1141269570]
Ugh no.  That is not the answer you want.  Continuously compounded interest.

Think about the number 'e', or click that link I posted.

[/quote]uh, I think thats the number I wanted.

like 10% of 50k after the first yr is 55k.  then add 10% of that for the next yr.

I don't think it is.  It is if interest is actually compounded only every year.  In almost every case, this is not so.  For example, if you invested $50000, you would probably have accumulated interest on it after a day, or a month, or two months.  The formula Yoni derived would suggest that your $50000 stays at exactly $50000 until after a year has passed.  This could very well be what was intended if it is some sort of obscure investment.  I would confirm, however, that they are not talking about expected gain of continuously compounded interest, compounded at a rate 'r = 10%' for a year.

Anyways, your total would be
1,004,276.85  if it is.

[quote author=Rule link=topic=14397.msg147426#msg147426 date=1141282024]
I don't think it is.  It is if interest is actually compounded only every year.  In almost every case, this is not so.  For example, if you invested $50000, you would probably have accumulated interest on it after a day, or a month, or two months.  The formula Yoni derived would suggest that your $50000 stays at exactly $50000 until after a year has passed.  This could very well be what was intended if it is some sort of obscure investment.  I would confirm, however, that they are not talking about expected gain of continuously compounded interest, compounded at a rate 'r = 10%' for a year.

Anyways, your total would be
1,004,276.85   if it is.



[/quote]

Too bad continuously compounded interest is not used often.  It would be faster to grow money since at every moment it is growing (rather than every month, quarter or year).

[quote author=Glove link=topic=14397.msg147436#msg147436 date=1141319930]
[quote author=Rule link=topic=14397.msg147426#msg147426 date=1141282024]
I don't think it is.  It is if interest is actually compounded only every year.  In almost every case, this is not so.  For example, if you invested $50000, you would probably have accumulated interest on it after a day, or a month, or two months.  The formula Yoni derived would suggest that your $50000 stays at exactly $50000 until after a year has passed.  This could very well be what was intended if it is some sort of obscure investment.  I would confirm, however, that they are not talking about expected gain of continuously compounded interest, compounded at a rate 'r = 10%' for a year.

Anyways, your total would be
1,004,276.85  if it is.



[/quote]

Too bad continuously compounded interest is not used often.  It would be faster to grow money since at every moment it is growing (rather than every month, quarter or year).
[/quote]

Which is why it is often used.  Think about it.  Interest rates are a lot higher on loans than on deposits in banks and on most investments.

[quote author=Rule link=topic=14397.msg147438#msg147438 date=1141320343]
[quote author=Glove link=topic=14397.msg147436#msg147436 date=1141319930]
[quote author=Rule link=topic=14397.msg147426#msg147426 date=1141282024]
I don't think it is.  It is if interest is actually compounded only every year.  In almost every case, this is not so.  For example, if you invested $50000, you would probably have accumulated interest on it after a day, or a month, or two months.  The formula Yoni derived would suggest that your $50000 stays at exactly $50000 until after a year has passed.  This could very well be what was intended if it is some sort of obscure investment.  I would confirm, however, that they are not talking about expected gain of continuously compounded interest, compounded at a rate 'r = 10%' for a year.

Anyways, your total would be
1,004,276.85   if it is.



[/quote]

Too bad continuously compounded interest is not used often.  It would be faster to grow money since at every moment it is growing (rather than every month, quarter or year).
[/quote]

Which is why it is often used.  Think about it.  Interest rates are a lot higher on loans than on deposits in banks and on most investments.

[/quote]

I have some understanding of the actuarial sciences.  It is rarely used there.  In fact, when I took an interest theory course, it wasn't even discussed.

I know that the 2 CDs I openned yesterday are compounded dailr, one at 4.2% & the other at 4.3% annual percentage

What?! No!!!
Rule, the page you linked is stupid. (Yes, if banks work that way, they're all stupid.)

[u]The formula they specify is:  FV(n)  =  P(1 + r/n)^(Yn)[/u]

According to that formula, if the yearly interest rate is 10%, and you pay quarterly instead of yearly, the quarterly interest rate becomes 2.5%! (0.1/4...)
That is clearly bullshit.
Interest rates are exponential. The interest rate should have become 1.1^(1/4) = 1.024.., or 2.4%.

Then, the correct formula becomes  FV(n)  =  P[(1 + r)^(1/n)]^(Yn)
If you calculate based on that assumption you will notice that continuous and discrete interest rates are the same.
(It's easy to notice that the n actually cancels out in the above formula... FV(n) is not dependent on n!)

[size=6]Yes, I assert that banks give you too much money because some idiot considered exponential interest rates as linear.[/size]

(You might want to listen to Rule instead of me if you want to get a good grade btw)

[quote author=Yoni link=topic=14397.msg147555#msg147555 date=1141436121]
What?! No!!!
Rule, the page you linked is stupid. (Yes, if banks work that way, they're all stupid.)

[u]The formula they specify is:  FV(n)   =   P(1 + r/n)^(Yn)[/u]

According to that formula, if the yearly interest rate is 10%, and you pay quarterly instead of yearly, the quarterly interest rate becomes 2.5%! (0.1/4...)
That is clearly bullshit.
Interest rates are exponential. The interest rate should have become 1.1^(1/4) = 1.024.., or 2.4%.

Then, the correct formula becomes  FV(n)   =   P[(1 + r)^(1/n)]^(Yn)
If you calculate based on that assumption you will notice that continuous and discrete interest rates are the same.
(It's easy to notice that the n actually cancels out in the above formula... FV(n) is not dependent on n!)

[size=6]Yes, I assert that banks give you too much money because some idiot considered exponential interest rates as linear.[/size]

(You might want to listen to Rule instead of me if you want to get a good grade btw)
[/quote]

See? Thank you.  Rarely anybody (if anybody) uses continous compound interest.

[quote author=Glove link=topic=14397.msg147580#msg147580 date=1141457995]
See? Thank you.  Rarely anybody (if anybody) uses continous compound interest.
[/quote]

Um, that's not what he was saying at all.  It seems that he was trying to redefine interest so there would be more consistency.  I'm not going to defend the people who came up with the standards we use for these things.

[quote author=Glove link=topic=14397.msg147580#msg147580 date=1141457995]
See? Thank you. Rarely anybody (if anybody) uses continous compound interest.
[/quote]
No, I don't know what people use. I wouldn't be surprised if people always use continuous compound interest. I am just making an effort of calling every actuarial scientist in the world an idiot over it, thus likely making a fool of myself once someone posts a really logical reason why continuous interest is defined that way.

We're doing this in math now.

If I was asked that question on an exam, I would use FV = PV(1+i)^n as Yoni mentioned, which is what we were taught to use.

FV = future value
PV = present value
i = 0.10/1 (10% interest rate compounded annually)
n = 30*1 (over period of 30 years, annual compounding)

FV = 50000(1+.10)^30
FV = 50000(17.45)
FV = $87,2470.11

Whether it would be a proper "school" response depends on a lot of things.  Stuff taught in school usually doesn't reflect what is practiced in the world -- various concepts are introduced mostly for pedagogical reasons.  Also, it depends what level of mathematics we're talking about.  The way continuously compounded interest is defined, it would be most appropriate to introduce it in
an advanced precalculus course, an introductory calculus course, or as a side note in an elementary differential equations course.

More importantly, Crazeds' question is vague.  There are different ways of calculating interest.  It is not clear in this instance whether the principal investment should be compounded "annually" at a rate of 10% (e.g. P*1.1^(N)), or compounded "continuously" at a rate of 10% for 30 years.  I lean towards the latter, since 'continuous compound interest' is what is usually used in the real world.

Its for a mutual fund.
Money goes into different investment things, I get more money back than I put in most of the time.  It isn't exactly a bank account or a CD with a set interest rate, its just the average rate for those 30 yrs.