It has been announced that railway fares will be raised by 10 percent starting on the first of March.

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.

What's the bus fare?

He paid double fare.

The fare is one dollar each way.

What's the bus fare?

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

Die, you wagehiking scum!

We share the recippe, we share the rent.

Discount rate

Now what can we do ?

Put this on your face, I'm gonna get you outside!

The comet leaves a trail of light behind it as it moves.

60 off.

We could have also done it other way.

Delivery is not included in the price.

Delivery isn't included in the price.

These are 30 percent off.

And it just depended on how the mathematics work out.

We could have said Let y equal the discount

5 minus this 2.

when the sale has a certain percentage ?

Because you're getting 10,000 from the bank.

And so this number right here, this number is the difference between those two numbers in 10 years, discounted back to today.

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.

Fifty percent of the Senate between 1998 and 2004

The cost of flying overseas has risen with the cost of fuel.

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.

So the next time you're looking at a charity, don't ask about the rate of their overhead.

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.

It's right over the rise. Bring it all back here.

Do you have a student fare?

Well, that was x.

But the big learning from this is how dependent the present value of future payments are on your discount rate assumption.

Negotiated prices is a dynamic price.

I have some coupons I got last week.