Homework SourseA Find the following values using the equations and then a f
A.)
Find the following values using the equations and then a financial calculator. Compounding/discounting occurs annually. Do not round intermediate calculations. Round your answers to the nearest cent.
An initial $200 compounded for 1 year at 4%.
An initial $200 compounded for 2 years at 4%.
The present value of $200 due in 1 year at a discount rate of 4%.
The present value of $200 due in 2 years at a discount rate of 4%.
B.)
An investment will pay $100 at the end of each of the next 3 years, $200 at the end of Year 4, $400 at the end of Year 5, and $600 at the end of Year 6.
If other investments of equal risk earn 4% annually, what is its present value? Round your answer to the nearest cent.
If other investments of equal risk earn 4% annually, what is its future value? Round your answer to the nearest cent.
Solution
A) 1) Future Value of 1 = (1+i)^n Where, i Interest rate n Life in years So, future Value of : An initial $200 compounded for 1 year at 4% = 200*(1+0.04)^1 = $ 208.00 An initial $200 compounded for 2 years at 4% = 200*(1+0.04)^2 = $ 216.32 2) Present Value of 1 = (1+i)^-n Where, i Interest rate n Life in years So,Present Value of: The present value of $200 due in 1 year at a discount rate of 4% = 200*(1+0.04)^-1 = $ 192.31 The present value of $200 due in 2 year at a discount rate of 4% = 200*(1+0.04)^-2 = $ 184.91 B) 1) Present Value of different annual cash flow is calculated as follows: Year Annual cash flow Discount factor Present Value a b c=1.04^-a d=b*c 1 $ 100 0.96154 $ 96.15 2 100 0.92456 $ 92.46 3 100 0.88900 $ 88.90 4 200 0.85480 $ 170.96 5 400 0.82193 $ 328.77 6 600 0.79031 $ 474.19 Total $ 1,251.43 2) Future Value of different annual cash flow is calculated as follows: Year Annual cash flow Discount factor Future Value a b c=1.04^(6-a) d=b*c 1 $ 100 1.21665 $ 121.67 2 100 1.16986 $ 116.99 3 100 1.12486 $ 112.49 4 200 1.08160 $ 216.32 5 400 1.04000 $ 416.00 6 600 1.00000 $ 600.00 Total $ 1,583.46
