We could have said Let y equal the discount

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

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.

This is the difference between the two.

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.

It's p.

Discount rate

Now what can we do ?

The nice mathematical thing about discount factor is it keeps this expectation bounded.

It easy to show that this expression over here will always be smaller or equal to 1 over 1 minus gamma times the absolute reward maximizing value and which in this case would be plus 100.

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

Anyway.

60 off.

That's the percentage off times the product in question, times the price, the non discount price of the product in question.

These are 30 percent off.

when the sale has a certain percentage ?

We could have also done it other way.

And it just depended on how the mathematics work out.

Free coupons. Discount Discount coupons.

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

Well, that's just positive 2, right?

We get plus 5 times x plus 4.

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

5 minus this 2.

Thirty percent off for USC alumni.

The Price to Earnings ratio is equal to the price so 3.50 divided by the earnings per share.

So once again we have verified, by taking the present value of 110 in 2 years to today, that its present value if we assume a 5 discount rate.

How much did you get for the deal?

Plus what's 25r divided by 5r?

And this is really just the sum of all the numbers divided by this is a human constructed definition that we've found useful the sum of all these numbers divided by the number of numbers we have.

Add that together with the gas, and it's 112,000 per year, just for that sign in each direction.

You would multiply thirty percent times the twenty dollars. so you would say your discount your discount is equal to, you could write is as 30 times 20.

Do you have a student fare?

Well, that was x.

It's positive 6f squared.

Is she still offering the twoforone discount?

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

We get a reward of zero in the old state.

Now you give me the price of any product in the store and I can substitute it in for x, and then I can essentially multiply it 0.3 times that and I would get the discount.

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 if you were to present value this let's say they make 1 forever going into the future and you were to present value this using a discount rate.

As I said we should be able to do all these pretty easy constant time.

A true false assignment to that variable..