1. **Problem Statement:** An investor plans to invest a single sum of 500000 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 if the investor wants to receive 500000 after 5 years at the same interest rate. 2. **Formulas and Rules:** - Future Value (FV) with compound interest is given by: $$FV = PV \times (1 + r)^n$$ where $PV$ is the present value, $r$ is the annual interest rate (in decimal), and $n$ is the number of years. - Present Value (PV) when future value is known: $$PV = \frac{FV}{(1 + r)^n}$$ - Interest rate 8% means $r = 0.08$. 3. **Calculations:** a) Calculate Future Value after 5 years: - Given $PV = 500000$, $r = 0.08$, $n = 5$ - Substitute into formula: $$FV = 500000 \times (1 + 0.08)^5$$ - Calculate inside the parentheses: $$1 + 0.08 = 1.08$$ - Raise to the power 5: $$1.08^5 = 1.4693280768$$ - Multiply: $$FV = 500000 \times 1.4693280768 = 734664.04$$ b) Calculate Present Value to get 500000 after 5 years: - Given $FV = 500000$, $r = 0.08$, $n = 5$ - Substitute into formula: $$PV = \frac{500000}{(1 + 0.08)^5} = \frac{500000}{1.08^5}$$ - Calculate denominator: $$1.08^5 = 1.4693280768$$ - Divide: $$PV = \frac{500000}{1.4693280768} = 340493.57$$ 4. **Final Answers:** - a) Future Value after 5 years is approximately **734664.04**. - b) Present Value needed to get 500000 after 5 years is approximately **340493.57**.