Interest Compounded Annually for 30 yrs.

[Yoni]

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

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

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!)

Yes, I assert that banks give you too much money because some idiot considered exponential interest rates as linear.

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

[Glove]

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

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

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!)

Yes, I assert that banks give you too much money because some idiot considered exponential interest rates as linear.

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

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

[Rule]

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

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.

[Yoni]

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

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.

[Spht]

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

[Rule]

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.

[CrAz3D]

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.