True of false + pls add a brief explanation

Statement: 1/ The price of a zero-coupon bond must increase as it approaches the maturity date because the power n in the denominator of (1 + r) n is decreasing.

2/ There are two bonds. The first bond is a 20 year US government zero-coupon nominal bond with a $1,000 par value. The second bond is a 20 year US government 1%- coupon nominal bond with a $1,000 par value. On March 24th, 2021, both bonds are correctly priced using zero-coupon yields from the Federal Reserve dataset we used in class. Statement: On March 24th, 2021, no rational investor is willing to buy the first bond, because its cash flows are lower than for the second bond