See practice question below - in the solution why does PV0 change in the denominator (it appears they have just dropped a 9)?

Thanks in advance!

Consider the following information for a traditional (option-free) fixed-rate bond where *PV*_{0} is the bond’s original price, *PV*_{+} is the new price of the bond when the yield to maturity is increased, *PV*_{−} is the new price of the bond when the yield to maturity is decreased, ∆Curve is the change in the benchmark yield curve, and ∆Yield is the change in the yield to maturity:

**PV _{0}**** PV

_{+}

**ΔYield** 99.41172 99.32213 99.50132 3 bps 1 bp**

**PV**_{−}**ΔCurve****Q.** The bond’s approximate convexity is *closest* to:

- 0.00101.
- 1.11769.
- 10.05918.

Solution

**C is correct.** The bond’s approximate convexity (ApproxCon) is 10.05918, calculated as:

ApproxCon = (PV−) + (PV + )−[2 × (PV0)] / (∆Yield)2 × (PV0) = 99.50132 + 99.322123−(2 × 99.41172) / (0.0001)2 × 9.41172 = 10.05918