1. **State the problem:** We want to find the initial amount $P$ to invest so that it grows to $A=650$ in $t=4$ years with an annual interest rate of $r=5.1\%$ compounded quarterly. 2. **Formula used:** The compound interest formula is $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where - $A$ is the amount after time $t$, - $P$ is the principal (initial investment), - $r$ is the annual interest rate (decimal), - $n$ is the number of compounding periods per year, - $t$ is the time in years. 3. **Identify values:** - $A = 650$ - $r = 5.1\% = 0.051$ - $n = 4$ (quarterly compounding) - $t = 4$ 4. **Rearrange formula to solve for $P$:** $$P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}$$ 5. **Calculate the denominator:** $$1 + \frac{0.051}{4} = 1 + 0.01275 = 1.01275$$ 6. **Calculate the exponent:** $$nt = 4 \times 4 = 16$$ 7. **Calculate the compound factor:** $$\left(1.01275\right)^{16} \approx 1.219006$$ 8. **Calculate $P$:** $$P = \frac{650}{1.219006} \approx 533.37$$ **Final answer:** The amount to invest now is approximately **533.37** rounded to the nearest cent.