Calculating total purchase price of bonds
About this video
An investor buys 20 Treasury bonds with a $2,000 face value, a 6.4% coupon and a market price quoted at 104.25% of face value, 37 days after the last interest payment, paying a $5 commission per bond. The video finds the price per bond (1.0425 x 2,000), adds the commission and the accrued interest (37/365 of the $128 annual coupon), and multiplies by 20 to get a total of about $42,059.51.
You'll be able to
- convert a bond price quoted as a percent of face value into dollars.
- calculate a bond's annual coupon payment from its coupon rate.
- calculate accrued interest a buyer pays the seller using days elapsed out of 365.
- find the total purchase price of several bonds including commission and accrued interest.
Key words
- Face value
- The amount a bond is worth at maturity, used to calculate its interest; here $2,000.
- Coupon rate
- The yearly interest rate a bond pays, as a percent of its face value.
- Market price
- What the bond sells for now, often quoted as a percent of face value.
- Accrued interest
- Interest earned since the last coupon payment that the buyer pays to the seller.
- Commission
- A fee paid to a broker for each bond bought or sold.
Transcript
- [Narrator] Federal infrastructure Treasury bonds have a face value of $2,000 per bond, a coupon rate of 6.4%, a current market price of $104.25. Actually, no I shouldn't say that. A current market price of 104.25 quoted as a percent of face value. An investor purchases 20 bonds 37 days after the last interest payment.
The commission is $5 per bond. What is the total purchase price, accounting for accrued interest and commission? Pause the video. Try to calculate that. All right, so there's several things we're gonna have to calculate. So first of all, just what is going to be the market price of the bond?
Well, it's going to be this percentage of the face value. So it would be 104% of $2,000, 104.25%. Or another way to think about it, it would be 1.0425 times $2,000, $2,000. So this is just what you're going to pay for. Let's just call it the... Before we consider the interest and the commission.
So that's that part right over there. And I'm doing everything per bond right now, plus we're gonna pay a commission of $5 per bond. That's pretty straightforward. Plus accrued interest. So this is what you need to appreciate is that bonds, this coupon rate, the coupon rate is what it pays off of the $2,000 per year.
So if you multiply 6.4% times $2,000, I think that is $128, if I'm doing my math correctly. It will pay that usually twice a year. Now, the thing to appreciate is when you buy a bond, the person who's selling it has essentially started to accrue some interest, but they haven't gotten the coupon for that yet.
So you have to pay them for that interest that they have accrued, that the government kind of owes them at that point in time. And so the way to calculate that is you say, okay, 37 out of 365 days have gone by. So that fraction of a year, in a year, the coupon in a year, the bond pays $2,000 times 6.4%.
So times $2,000 times $2,000 times 6.4%, 0.064. This will give the payment of accrued interest that you have to pay per bond because of 37 out of the 365 days, it's that fraction of the year. And this is how much the coupon payment is for the full year. And so if we calculate all of this, this would be the purchase price per bond.
And then of course we would wanna multiply all of that times 20 'cause we got 20 bonds. So let me get a calculator out and let's actually calculate this. Maybe I'll get a graphing calculator out since I can see what I'm doing a little bit more clearly. So turn it on.
All right, so I'm gonna open parentheses. 1.0425 times 2,000. That says 20,000 there, but I know it's 2,000. I'll change that when I get off of that. Not 20, that's weirdly placed comma too. Okay, I have that. Order of operations, it'll do that multiplication first, so that's fine.
So then plus $5, plus, and I have to just multiply all of this stuff or do a little bit of dividing. 37 divided by 365 times 2,000 times 0.064. And I'm gonna close the parentheses and I'm now going to multiply by 20, times 20 is equal to 42,000... Let me put this on the side.
And so that is equal to, and let me correct this. I put an extra zero here, ignore that zero. But all of this is equal to $42,000 or $42,059. And if I round, I get to 51 cents. That's the total amount, total purchase price for the 20 bonds, including accrued interest.
That's this part right over here, and commission right over there.
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