If $7,000 is invested at 20% annual simple interest, how long does it take to be worth $33,600?

1. Use the simple interest formula: A = P(1 + rt)

2. Substitute the given values: 33,600 = 7,000(1 + 0.20 \times t)

3. Simplify: 1 + 0.20t = \frac{33,600}{7,000}

4. Calculate: 1 + 0.20t = 4.8

5. Rearrange: 0.20t = 4.8 - 1

6. Simplify further: 0.20t = 3.8

7. Solve for t : t = \frac{3.8}{0.20}

8. Calculate the result: t = 19

Thus, the time it will take is t = 19 years.