So then you go [LAUGH] if you wait a full year you can come back to the bank and

now you get $103, now your account is marked up for compounding.

If you go back to the bank in 18 months since you deposited it, and

you ask for your money, they'd say well now you have $103 [LAUGH]

because we haven't credited your new interest for this year.

You have to wait two years and after two years how much do you have?

You have 1.03 times $1.03,

is little over $1.06, if you have annual compounding.

Now the banks often compound more often than once a year so

suppose they compound twice per year.

You put in $100 in a 3% compounding twice per year, if you went to get your money in

the first six months, you would still just get $100 back.

After six months, you'd get $101.50,

if you went back after nine months, you'd get $101.50.

You'd have to wait two years, no, one full year, did I say that right?

Yeah, you'd have to wait a full year and

then you would get 1.015 squared times $100.

You see where we're going on this, if it's compounded twice

per year the balance is 1 plus r over 2 times 2t after t years.

Where t is any number, which is either one or,

one plus, it's either an integer or

an integer plus a half, in between it's a step function.

And if it's compounded n-times a year,

the balance is one plus r over n to the nt-th period.

Now if you take the limit of this expression as n goes to infinity,