The probability of reaching S prime given that we started state S and apply action A.

Discount rate

Now what can we do ?

60 off.

We could have also done it other way.

These are 30 percent off.

And it just depended on how the mathematics work out.

Another way to kind of just talk about this is to get the present value of 110 a year from now, we discount the value by a discount rate.

We could have said Let y equal the discount

5 minus this 2.

when the sale has a certain percentage ?

And this one that was in Kenya, they went around and distributed to people vouchers, discount vouchers.

Free coupons. Discount Discount coupons.

Well, I don't give group rates, you know.

Are there special evening rates?

If I could get it for 90, that's a good deal for me.

So x minus twenty five percent x is equal to the sale price.

But what if I wanted to generalize a little bit ?

Special rates for state and federal employees.

Then to discount money in the future to the present, we divide it by 1 plus the discount rate so this is a 5 discount rate.

Let's say in every year it's going to make 1.

Thirty percent off for USC alumni.

Be silent. Keep your forked tongue behind your teeth.

Do you have a student fare?

Well, that was x.

I have some coupons I got last week.

So 2009 money, that's worth 1.

Let x be the price of the product I want to buy, the nondiscount price of the product in the store.

What is it about Superman?

I bought the car at a 10 discount.

This is the difference between the two.

To compound the amount of money we invest we multiply the amount we invest times 1 plus the yield.

The store offered special discounts during the summer.

I get a discount and there's a whole section of books in my area.

It's all assumption driven.

Are there any discount tickets for me?

I thought we had discussed a cash discount.

It's p.

Well the antiderivative of y squared and you have to divide by 3, so it's y cubed over 6.

I'll say p, just so it makes sense, p is equal to the percentage off.

Perhaps only at a discount.

You should discount his story.

You'd better take his words with a grain of salt.

Now this is really interesting, now we have a general way of calculating a discount for any given percentage off and any given product x.

But let's generalize even more.