Question

An investment will pay $50 at the end of each of the next 3 years, $250 at the end of Year 4, $350 at the end of Year 5, and $500 at the end of Year 6.
If other investments of equal risk earn 7% annually, what is its present value? Its future value? Do not round intermediate calculations. Round your answers to the nearest cent.

Answer 1

Answer:

• A) Present value = $ 904.66

• B) Future value = $ 1,357.65

Explanation:

A) Present value

You must discount each cash flow (payment) according to the moment when it is paid, at the same rate of return of other investments fo equal risk: 7%.

• Year 1: $50

• Year 2: $50

• Year 3: $50

• Year 4: $250

• Year 5: $350

• Year 6: $500

Thee formula that you must use is:

            $PV=\frac{CF_1}{(1+i)^1}+\frac{CF_2}{(1+i)^2}+\frac{CF_3}{(1+i)^3}+\frac{CF_4}{(1+i)^4}+\frac{CF_5}{(1+i)^5}+\frac{CF_6}{(1+i)^6}$

         

Where PV is the present value; CF₁, CF₂, CF₃, CF₄, CF₅, and CF₆ are the cash flows of the years 1, 2, 3, 4, 5, and 6 respectively, and i is the annual return.

Substituting:

$PV=\frac{50}{(1+0.07)^1}+\frac{50}{(1+0.07)^2}+\frac{50}{(1+0.07)^3}+\frac{250}{(1+0.07)^4}+\frac{350}{(1+0.07)^5}+\frac{500}{(1+0.06)^6}$

Computing:

          $PV=\ 904.66$

B) Future value

The formula for future value is:

         $FV=PV(1+r)^t$

Where, FV is the future value to calculate; PV is the present value already calculated, r is the rate of return, 7% = 0.07); and t is the number of periods, 6 years.

Substituting and computing:

         $FV=\ 904.66\times (1+0.07)^6\\\\FV=\ 1,357.65$