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

• A) Present value = $ 904.66

• B) Future value = $ 1,357.65

Step-by-step 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=(CF_1)/((1+i)^1)+(CF_2)/((1+i)^2)+(CF_3)/((1+i)^3)+(CF_4)/((1+i)^4)+(CF_5)/((1+i)^5)+(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=(50)/((1+0.07)^1)+(50)/((1+0.07)^2)+(50)/((1+0.07)^3)+(250)/((1+0.07)^4)+(350)/((1+0.07)^5)+(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* (1+0.07)^6\\\\FV=\$ 1,357.65`