How do I loop for only specific "case" in switch/case?

You can have one boolean variable for getting out of while-loop. Flag is set to false in switch/case because while(false) wont iterate further.

boolean flag = true;
while(flag){
    switch(bank){
        case "A","C":
            System.out.println("You can make $" + (Math.round((0.015 * money)*100)) / 100.0);
            flag = false; //put this in all case.
            break;
        ...
    }
}

package com.javatutorial;

import java.util.Scanner;

class Main{
    public static void main(String[] args) throws Exception
    {
        String bank = "";
        double money = 0;
        boolean valid = false;

        Scanner myinput = new Scanner (System.in);
        System.out.print("Please enter the amount of money you want in the bank: ");

        while (true) {
            try {
                money = myinput.nextDouble();
                break;
            } catch (Exception e) {
                System.out.println("This is inappropriate. Please enter the amount of money you want in the bank: ");
                myinput.next();
            }

        }

   do {
       System.out.println("Please enter the type of account you want: ");
       bank = myinput.next();
        switch (bank) {

            case "A":
            case "C":
                System.out.println("You can make $" + (Math.round((0.015 * money) * 100)) / 100.0);
                valid = true;
                break;
            case "B":
                System.out.println("You can make $" + (Math.round((0.02 * money) * 100)) / 100.0);
                valid = true;
                break;
            case "X":
                System.out.println("You can make $" + (Math.round((0.05 * money) * 100)) / 100.0);
                valid = true;
                break;
            default:
                System.out.println("This is inappropriate input. Please enter the type of account you want");
        }
    }while( !valid);

    }
}