So now we're going to make this idea more general.

So, we've gone out through three years what if you wanted to go

out through n years.

So n being whatever number you want it to specify.

Well then the Future Value in n years which we're going to call FV so

anytime you see FV that stands for Future Value n years from now,

that's going to equal to a 100 times 1.08 raised to the nth power.

So a way to think about that is if you wanted to do this for 10 years.

It would be 100 times 1.08 ten times.

You'd multiply it time, ten times over.

If n was 20, it'll be 100 times 1.08, 20 times.

So you can put in whatever period you want in the exponent.

[SOUND] If the CD paid r% interest instead of 8% interest,

then the future value is going to be 100 times 1 plus r raised to the n.

So now we caould try this with 3% or 10% or 1%.

If it was 1%, then it would be 1.01.

And then if it was five years it would be raised to the fifth power.

So you can specify whatever interest rate you want, whatever peerage you want.

And then if your initial investment was $PV instead of a $100,

here PV is going to stand for Present Value or today's value.

Then we have future value equals present value, times 1 plus r to the n,

and that gets us to the general formula that we can use for

any level of in, initial investment, any interest rate, or any number of years or

number of periods that we're going to have the money invested.

So again, [NOISE] the terminology, Present Value, PV,

of what you invest today is going to grow at an interest rate r,

to earn a Future Value, FV, n years from now,

using this formula FV equals PV times 1 plus r raised to the n power.

>> Okay, this makes sense.

Will there also be a formula to compute past values?

Or does this formula just work going into the future?

>> No we won't have a separate formula for past values, because

as it turns out you can use the same formula to calculate values in the past.

So I'll talk about on the next slide the terminology, but what you'll see is.

Present value doesn't necessarily need to mean today, it could mean 20 years ago,

and future value could be today.

So just think of it as, present value and future value as before and

after we have things grow or compound, as I'll shown on the next slide.