# Dirty Price / Clean Price

Suppose that a bond is purchased between coupon periods. The days between the settlement date and the next coupon period are 115. There are 183 days in the coupon period. Suppose that the bond purchased has a coupon rate of 7.4% and there are 10 semiannual coupon payments remaining.

A) What is the dirty price for this bond if a 5.6% discount rate is used?

The answer says to start by solving for the Clean Price, and they have n = 9.6284?? – where does that come from?

There are 115 days out of 183 until the next coupon payment; 115 ÷ 183 = 0.628415, so that’s where they got the fraction.

Remember that the last coupon payment occurs at maturity: n = 0. If there are 10 payments left, they come at times (counting back from maturity) 0, 1, 2, . . ., 9, and there is 0.6284 of a period until the first one; hence: 9.6284.

If you draw a timeline, you’ll see this instantly.

I have yet to encounter any quesitons where N was not a whole number. Maybe these are the ones i got wrong? do you have any more examples and have the Full answer for the previous question?

Thanks!