An investment will pay $100 at the end of each of the next 3 years, $400 at the end of Year 4, $600 at the end of Year 5, and $700 at the end of Year 6. If other investments of equal risk earn 8% annually, what is its present value?
What is its future value? Round your answer to the nearest cent.
Answer: 2203.51
To find the present value of an investment, you need to discount the future cash flows back to the present using the appropriate discount rate. In this case, we have the cash flows occurring at different points in time, so we need to discount each cash flow separately.
The future value of the investment can be found by summing up the future cash flows. In this case, we have $100 at the end of each of the next 3 years, $400 at the end of Year 4, $600 at the end of Year 5, and $700 at the end of Year 6.
To find the present value, we can use the formula:
PV = CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 + CF4/(1+r)^4 + CF5/(1+r)^5 + CF6/(1+r)^6
where PV is the present value, CF is the cash flow at each period, r is the discount rate.
So, plugging in the values, we have:
PV = $100/(1+0.08)^1 + $100/(1+0.08)^2 + $100/(1+0.08)^3 + $400/(1+0.08)^4 + $600/(1+0.08)^5 + $700/(1+0.08)^6
Simplifying this equation will give us the present value.
PV ≈ $100/1.08^1 + $100/1.08^2 + $100/1.08^3 + $400/1.08^4 + $600/1.08^5 + $700/1.08^6
Calculating this expression will give us the present value of the investment. In this case, it is approximately $2203.51.
Therefore, the present value of the investment is $2203.51.
Note: The future value in this case would be the sum of all the future cash flows, which is $100 + $100 + $100 + $400 + $600 + $700 = $2000.
To calculate the present value of the investment, we need to discount each cash flow to its present value using the formula: PV = CF / (1 + r)^t.
Given that the annual interest rate is 8%, and the cash flows are as follows:
Year 1: $100
Year 2: $100
Year 3: $100
Year 4: $400
Year 5: $600
Year 6: $700
Using the formula, we can calculate the present value of each cash flow:
Present value of Year 1 cash flow = $100 / (1 + 0.08)^1 = $92.59
Present value of Year 2 cash flow = $100 / (1 + 0.08)^2 = $85.73
Present value of Year 3 cash flow = $100 / (1 + 0.08)^3 = $79.38
Present value of Year 4 cash flow = $400 / (1 + 0.08)^4 = $301.88
Present value of Year 5 cash flow = $600 / (1 + 0.08)^5 = $421.66
Present value of Year 6 cash flow = $700 / (1 + 0.08)^6 = $450.27
To find the present value of the investment, we sum up the present values of all the cash flows:
Present value = $92.59 + $85.73 + $79.38 + $301.88 + $421.66 + $450.27 = $1431.51
Therefore, the present value of the investment is $1431.51.
To calculate the future value of the investment, we can use the formula: FV = PV * (1 + r)^t.
Using the present value of $1431.51 and an annual interest rate of 8%, we can calculate the future value:
Future value = $1431.51 * (1 + 0.08)^6 = $1431.51 * 1.59385 = $2281.14
Rounded to the nearest cent, the future value of the investment is $2281.14.