In this workout, we're told that the US Treasury has just auctioned 10 billion US dollar notional of a five year bond, and the blow bids have been collected.

Assuming the coupon for the auctioned bond is set at 4.5%, at which price would the bond be sold to investors? Remember that US treasuries pay semi-annual coupons.

So we've got lots of information here and we're told that at a relatively low yield of 4.522% demand or even aggregate demands will only be 3.4 billion at a slightly higher yield, 4.523%.

We get up to 8.3 aggregate demand, but it's only when the yield goes to 4.524%, the aggregate demand goes over that 10 billion and the full amount is auctioned.

So the issue yield is the first thing we need to fill in, and it was that 4.524%.

That's where all of the auction is completed.

So now I need to come up with the price.

That yield will be the discount rate I use to present value the cash flows.

Once I then sum up the present value of cash flows, I'll have the price.

So let's start with those cash flows.

Well, the first thing we're going to get are the coupons and we'll get 4.5%.

Uh, but hang on, this is going to be paid semi-annually, so I'll lock onto that and then divide that by the two.

That's 2.225%.

That's going to be paid over 10 periods 'cause it's a five year bond and it's paid semi-annually.

So that's 10 periods. I can copy that down.

And in the final period we'll get our money back.

So what I'll do is I'll go into the formula and I'll just add on a one.

So I get 102.25% back at the end.

Now to present value, I take the cashflow and I'm going to divide it by one plus the discount rates.

And our discount rates.

That was the issue yield that we calculated earlier.

And I'll lock onto that.

That's for a full year though, and we need to discount it for six months.

So I'll divide that by two, close the brackets, and now put it to the power of the period that I'm in.

Excellent. I'll copy that down.

And now I'll sum them all up at the bottom, getting me to a price of 99.8937%.