1. **State the problem:** Corinne wants to have $30,000 in 12 years by investing now in a CD with 4.95% interest compounded quarterly. 2. **Formula used:** The formula for compound interest is $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount of money accumulated after $t$ years, including interest. - $P$ is the principal (initial investment). - $r$ is the annual interest rate (decimal). - $n$ is the number of times interest is compounded per year. - $t$ is the time the money is invested for in years. 3. **Identify values:** - $A = 30000$ - $r = 0.0495$ - $n = 4$ (quarterly compounding) - $t = 12$ 4. **Rearrange formula to solve for $P$:** $$P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}$$ 5. **Calculate:** $$P = \frac{30000}{\left(1 + \frac{0.0495}{4}\right)^{4 \times 12}} = \frac{30000}{\left(1 + 0.012375\right)^{48}} = \frac{30000}{(1.012375)^{48}}$$ 6. Calculate the denominator: $$(1.012375)^{48} \approx 1.718186$$ 7. Calculate $P$: $$P = \frac{30000}{1.718186} \approx 17466.88$$ **Answer:** Corinne should invest approximately $17466.88 now to reach her goal of $30000 in 12 years.