When we do these calculations,

there's going to be an interest rate that is going to govern this calculation.

And for now,

we're going to assume that that interest rate is the same every period.

Okay and we'll denote the interest rate by R.

Now, I'm going to start out by talking about future values,

because I think sometimes, there's more intuition associated with that.

So, if you wanted to know what the future value of cash that you have on hand is.

That you are going to say, deposit in a bank account.

The way that you would calculate what the value of that cash would be at period n.

Is to take the cash that you're going to deposit in the bank today.

The present value and multiply that by one plus r raised to the nth power.

So what would be an example of this?

Well, suppose that there was a bank account around and

that interest rate on that bank account was 10% per year.

And you wanted to know what amount of money you would have in the bank at

the end of one year.

If you deposited $1000 in the bank today and so,

applying that formula, what would we do?

Well, what we're trying to calculate is we're trying to calculate F sub one.

So, you would take the amount of money that you're depositing

in the account today $1,000.

And you would multiply it by one plus the interest rate of 10%,

which of course 10% is 0.1.

And so, you're taking a thousand and you're multiplying it by 1.1.

What that means is, at the end of the year, you would have $1,100 in the bank,

right.

So you'd deposit $1,000 today.

Over the year, you earn interest at 10% per year, and

at the end of the year you have $1,100.

That is the future value of that $1,000 a year from today.

When there's a bank account around that pays you at the rate of 10% per year.

Now, what if you wanted to ask the question of what amount of money would

you have in that same bank account if you left that money in there for two years?