解：(1)設(shè)該商場投入資金的月增長率為$x.$
根據(jù)題意，得$20(1 + x)^2 = 24.2，$
即$(1 + x)^2 = 1.21，$
則$1 + x = \pm1.1，$
當(dāng)$1 + x = 1.1$時(shí)，$x = 0.1 = 10\%；$
當(dāng)$1 + x = -1.1$時(shí)，$x = -2.1$（不合題意，舍去）.
答：該商場投入資金的月增長率為$10\%.$
(2)$24.2×(1 + 10\%) = 24.2×1.1 = 26.62$（萬元）.
答：預(yù)計(jì)該商場七月份投入資金將達(dá)到$26.62$萬元.
