1. **Problem Statement:** An investor plans to invest a single sum of 250000 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: $$PV = \frac{FV}{(1 + r)^n}$$ 3. **Calculations:** a) Calculate Future Value after 5 years: - Given: $PV = 250000$, $r = 0.08$, $n = 5$ - Substitute into formula: $$FV = 250000 \times (1 + 0.08)^5$$ - Calculate: $$FV = 250000 \times (1.08)^5$$ - Compute $(1.08)^5$: $$1.08^5 = 1.46933$$ (rounded to 5 decimal places) - Multiply: $$FV = 250000 \times 1.46933 = 367332.5$$ - So, the future value after 5 years is **367332.5**. b) Calculate Present Value to get 500000 after 5 years: - Given: $FV = 500000$, $r = 0.08$, $n = 5$ - Substitute into formula: $$PV = \frac{500000}{(1 + 0.08)^5} = \frac{500000}{1.46933}$$ - Calculate: $$PV = 340430.5$$ (rounded to 1 decimal place) - So, the present value needed is **340430.5**. **Final answers:** a) Future Value = 367332.5 b) Present Value = 340430.5