1. **State the problem:** Robert wants to save 50000 in 5 years with an annual interest rate of 4% compounded monthly. We need to find the present value (initial investment) he should invest today. 2. **Formula used:** For compound interest compounded monthly, the future value $A$ is given by: $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $P$ is the principal (initial investment), - $r$ is the annual interest rate (decimal), - $n$ is the number of compounding periods per year, - $t$ is the number of years. 3. **Given values:** - $A = 50000$ - $r = 0.04$ - $n = 12$ - $t = 5$ 4. **Rearrange formula to solve for $P$:** $$P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}$$ 5. **Substitute values:** $$P = \frac{50000}{\left(1 + \frac{0.04}{12}\right)^{12 \times 5}}$$ 6. **Calculate inside the parentheses:** $$1 + \frac{0.04}{12} = 1 + 0.0033333 = 1.0033333$$ 7. **Calculate the exponent:** $$12 \times 5 = 60$$ 8. **Calculate the power:** $$1.0033333^{60} \approx 1.221392$$ 9. **Calculate $P$:** $$P = \frac{50000}{1.221392}$$ 10. **Simplify:** $$P \approx 40918.68$$ **Answer:** Robert should invest approximately **40918.68** today to reach his goal of 50000 in 5 years with 4% annual interest compounded monthly.