The graph of the balance of an investment is given. You can vary the initial value, annual percentage rate (APR), and the number of compounding periods per year to change the curve. Also you can use the Time sider and Target Value sider to see how long it takes for the balance to reach the target value. Initial value $250 APR 10% Type ot Conipounding annual semiannual quarterly monthly Balance (dollars) 10,000- 9,000 - 8,000 7,000- 6,000- 5,000- 4,000- 3,000- 2,000- 1,000- 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time (years) daly Time 6 Target value 8,000 Compounding annual semiannual quarterly monthly dally Time 6,000 5,000- 4,000 Balance (dolla 3,000 2,000 1,000 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time (years) Target value 8,000 Questions 1. Given an initial value of $200, for what combinations of rates and compounding could you reach your target value of $1000 within 10 years? 2. List three different combinations of variables that will allow you to achieve a target value of $3000. 3. No matter what your initial conditions and target value happen to be, are you always guaranteed to reach your goal within 15 years? 4. If your target value is $5000, and you begin with an initial investment of $500 and an APR of 1696, how long would it take to get halfway to your goal