1. **Problem statement:** An investor plans to invest a single sum of 250000 at an annual interest rate of 6%, compounded annually. a) Calculate the future value after 5 years. b) Calculate the present value needed to have 500000 after 5 years at the same interest rate. 2. **Formula used:** The formula for compound interest is: $$FV = PV \times (1 + r)^n$$ where: - $FV$ is the future value - $PV$ is the present value (initial investment) - $r$ is the annual interest rate (in decimal) - $n$ is the number of years To find present value when future value is known: $$PV = \frac{FV}{(1 + r)^n}$$ 3. **Calculations for part (a):** Given: - $PV = 250000$ - $r = 0.06$ - $n = 5$ Calculate future value: $$FV = 250000 \times (1 + 0.06)^5$$ Calculate the growth factor: $$1 + 0.06 = 1.06$$ Raise to the power 5: $$1.06^5 = 1.3382255776$$ Multiply: $$FV = 250000 \times 1.3382255776 = 334556.39$$ So, the future value after 5 years is approximately 334556.39. 4. **Calculations for part (b):** Given: - $FV = 500000$ - $r = 0.06$ - $n = 5$ Calculate present value: $$PV = \frac{500000}{(1 + 0.06)^5} = \frac{500000}{1.3382255776}$$ Divide: $$PV = 373460.15$$ So, the investor needs to invest approximately 373460.15 now to have 500000 after 5 years. **Final answers:** a) Future value = 334556.39 b) Present value = 373460.15