Question

compound interest, what is the difference?

Answer 1

what do I get from each one?

Answer 2

@mathmale hey, can you help here?

Answer 3

Hi, Lucaz,

The first formula is just a special case of the second. We'll get back to that in a moment.
The second formula is the most general and most useful when you want to discuss compound interest.

Answer 4

what I know is that the first one gives the future value after t years, and the last one we get the number e

Answer 5

Darn! Equation Editor isn't working; I was going to use that to continue our discussion.

Answer 6

The second formula applies when your interest rate is r and when interest is paid n times per year.

Answer 7

For example, suppose that your bank pays you interest on your funds 4 times per year (compounded quarterly). Then n=4. Suppose that interest is 8% per year, or 0.08 (wishful thinking nowadays). Then If the dollar amount you begin with is P=$100, you'll end up with A=P(1+0.08/4)^(4t) dollars after t years. Bet you've seen and heard this before.

Answer 8

in this case the interest must be annualy?

Answer 9

to use this formula P(1+r/n)^nt?

Answer 10

sorry for the delay!

Answer 11

its okay

Answer 12

yes, "r" always represents annual interest.

The first formula is for interest paid and compounded once per year; n=1. Then

A=P(1+r)^t.
This is the same thing as

Answer 13

A=P(1+r/n)^(nt) where n=1.

Answer 14

oh, I see

Answer 15

Now for the third: Not sure (have to look it up on the Internet): Were we to let n get larger and larger without limit, that expression would eventually give us

A=Pe (which is not very useful without t (time)).

When interest is compounded constantly (which does happen sometimes),

A=Pe^(rt), where r is the annual interest rate expressed as a decimal fraction.

Answer 16

Think about this discussion. All clear for you? Further questions about it?

Answer 17

you helped a lot, I get it now
thank you!

Answer 18

De nada. Con mucho gusto. My great pleasure. Buenos dias.