Interest Compounded Annually for 30 yrs.

[CrAz3D]

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

[Rule]

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.

[K]

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

[CrAz3D]

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

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.

[Rule]

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

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

[topaz]

10% interest rate?! WHAT BANK?!

[Yoni]

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

[CrAz3D]

10% interest rate?! WHAT BANK?!

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!

[Rule]

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

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

[CrAz3D]

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

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

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.

[Rule]

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.

[Glove]

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.

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).

[Rule]

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.

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).

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.

[Glove]

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.

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).

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.

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.

[CrAz3D]

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