We took a break from the Catechism during the school break, but hit it again on Monday of this week when school started back up. These are great questions!
Question #59: What good does it do you, however, to believe all this?
Answer: In Christ I am right with God and heir to life everlasting (1 John 3:36; Rom. 1:17, Hab. 2:4; Rom. 5:1-2).
Question #60: How are you right with God?
Answer: Only by true faith in Jesus Christ. Even though my conscience accuses me of having grievously sinned against all God's commandments and of never having kept any of them, and even though I am still inclined toward all evil, nevertheless, without my deserving it at all, out of sheer grace, God grants and credits to me the perfect satisfaction, righteousness, and holiness of Christ, as if I had never sinned nor been a sinner, as if I had been as perfectly obedient as Christ was obedient for me. All I need to do is to accept this gift of God with a believing heart (1 Rom. 3:21-28; Gal. 2:16; Eph. 2:8-9; Phil 3:8-11, Rom. 3:9-10, Rom. 7:23, Tit. 3:4-5, Rom. 3:24; Eph. 2:8, Rom. 4:3-5 (Gen. 15:6); 2 Cor. 5:17-19; 1 John 2:1-2, Rom. 4:24-25; 2 Cor. 5:21, John 3:18; Acts 16:30-31).
Question #61: Why do you say that by faith alone you are right with God?
Answer: It is not because of any value my faith has that God is pleased with me. Only Christ's satisfaction, righteousness, and holiness make me right with God. And I can receive this righteousness and make it mine in no other way than by faith alone (1 Cor. 1:30-31, Rom. 10:10; 1 John 5:10-12)