Calculate the price of a zero-coupon, semi-annual bond using an actual/actual calendar basis. The bond was purchased on May 19, 2016 and will mature on January 31, 2030, and has a yield to maturity of 7%.
"Zero coupon" means that no interest is paid on this bond until maturity. The bond will mature at par value or $100. Basically, what you do here is to find the PV of that $100 par value at maturity. You have to calculate the number of semi-annual periods between the maturity date and the purchase date. There are 27 even semi-annual periods and 1 odd period between Nov. 19, 2029 and the maturity date of Jan. 31, 2030. There are 73 days between those two dates. And there are 181 days in the last semi-annual period between Nov. 19, 2029 and May 19, 2030.
So, we have 27 semi-annual periods + 73/181 =27.4033149 periods.
So, now we use the common TVM formula:
PV=FV [1 + .07/2]^-27.4033149
PV=100 x 0.3896
PV=$38.96 The price of this zero coupon bond.
