# selling price of bonds

#### missl

##### New member
Hey does anyone know if the n: is 2*2 =4 because of the selling price of bond is april 18, 2007 and mature on aug 1, 2009 or do we count as apri 18 to aug 1?

A bond with a face value of $1,000 bears interest at 10% payable semi-annually. The bond matures on August 1, 2009. What is the selling price of the bond on April 18, 2007, to yield 9% compounded semi-annually? #### stapel ##### Super Moderator Staff member As has been mentioned in various of your other threads, the "n" refers to the number of compoundings per interest-rate period. For instance, if the interest rate is quoted as being "annual", then the interest-rate period is one year. Then if the interest were compounded monthly, n would be 12, because there are twelve months in one year. If the interest were compounded quarterly, then n would be 4, because "quarter" means "one-fourth", and there are four fourths (four quarters) in one year. If the interest were compounded daily, then n would be 360, 365, 366, or 365.25, depending on how a "year" is defined (by the bank and/or contract) in terms of the number of days. I hope this clarifies this issue for you. Eliz. #### Denis ##### Senior Member missl said: A bond with a face value of$1,000 bears interest at 10% payable semi-annually. The bond matures on August 1, 2009. What is the selling price of the bond on April 18, 2007, to yield 9% compounded semi-annually?
This is what the cash flows look like:
Code:
Apr18/07       Aug1/07       Feb1/08       Aug1/08         Feb1/09           Aug1/09
PV = ?            50            50            50             50             50 + 1000
So you need the PV of 5 semiannual payments of 50, plus the PV of 1000 for 5 semiannual periods; so N = 5.
This will give the PV (or selling price) AS AT Feb1/07.
To calculate as at Apr 18th depends on the method agreed upon:
in my days, we'd take days from Feb 1st to Apr 18th: 27 + 31 + 18 = 76;
then the days from Feb1/07 to Aug1/07: make it 182 (I ain't counting 'em!)

We would then add 76/182 * 50 = ~20.87 to the purchase price (since we had earned that portion).

What can I say :shock:

#### missl

##### New member
Okay I kind of get it. But where does the Feb comes in? :?

#### Denis

##### Senior Member
missl said:
Okay I kind of get it. But where does the Feb comes in? :?
You seem to be complicating things that are simple!
If it's semi-annual, then it's TWICE per year, or every 6 months, right?
If Aug 1st is the date of 1 of those 2 periods, then what is the other?