1. **Problem Statement:** An investor plans to invest a single sum of 300000 at an annual interest rate of 8%, compounded annually. a) Calculate the future value of the investment after 5 years. b) Calculate the present value needed to receive 500000 after 5 years at the same interest rate. 2. **Formulas and Rules:** - Future Value (FV) formula for compound interest: $$FV = PV \times (1 + r)^n$$ where $PV$ is the present value, $r$ is the annual interest rate (in decimal), and $n$ is the number of years. - Present Value (PV) formula when future value is known: $$PV = \frac{FV}{(1 + r)^n}$$ - Interest rate must be converted from percentage to decimal by dividing by 100. 3. **Calculations:** a) Calculate Future Value after 5 years: - Given: $PV = 300000$, $r = 8\% = 0.08$, $n = 5$ - Substitute into formula: $$FV = 300000 \times (1 + 0.08)^5$$ - Calculate: $$FV = 300000 \times (1.08)^5$$ $$FV = 300000 \times 1.4693280768$$ $$FV \approx 440798.42$$ b) Calculate Present Value to get 500000 after 5 years: - Given: $FV = 500000$, $r = 0.08$, $n = 5$ - Substitute into formula: $$PV = \frac{500000}{(1 + 0.08)^5}$$ - Calculate: $$PV = \frac{500000}{1.4693280768}$$ $$PV \approx 340352.24$$ 4. **Final Answers:** a) The future value of the investment after 5 years is approximately 440798.42. b) The present value needed to receive 500000 after 5 years is approximately 340352.24.