Please help to illustrate how to come up with a variance of 1.99 and 4.06 in the following example:

Compare the interest risk of the following two bonds with different maturity, but the same face value, same coupon rate, the same year to maturity (YTM)

1) Suppose a two-year zero-coupon bond has a face value of 100. Calculate the bond price at issuance when the YTM is 4%, 5%, or 6%.

Answer:

4%: P0 = 100/(1+0.04)2=92.46.

5%: P0 = 100/(1+0.05)2=90.71. 6%:

P0 = 100/(1+0.06)2=89.00.

Variance: 1.99.

2) Suppose a three-year zero-coupon bond has a face value of 100. Calculate bond price at issuance if the YTM is 4%, 5%, or 6%.

Answer:

4%: P0 = 100/(1+0.04)3=88..90.

5%: P0 = 100/(1+0.05)3=86.38.

6%: P0 = 100/(1+0.06)3=83.96.

Variance: 4.06.