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

This is the difference between the two.

We give a 10 discount for cash.

Will you give any discount if I pay in cash?

I thought we had discussed a cash discount.

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.

Discount rate

Now what can we do ?

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

60 off.

Anyway.

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.

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.

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

We could have said Let y equal the discount

5 minus this 2.

Thirty percent off for USC alumni.

Body split counts

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.

Do you have a student fare?

Well, that was x.

And then some of its payment is today.

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

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.

Berkeley, California September '08 Part 3

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

Pay now,or nothing.

Are there any discount tickets for me?

But what if I wanted to generalize a little bit ?

Be silent. Keep your forked tongue behind your teeth.

Special rates for state and federal employees.

How can we change the practices?

And that's cash on delivery, not check on delivery.

Is she still offering the twoforone discount?

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

Baryonic fraction, in clusters of galaxies.

I have some coupons I got last week.

So 2009 money, that's worth 1.