A project requires an initial investment of $7,000, and is guaranteed to yield a return of $1,500 at the end of the first year, $2,500 at the end of the second year and $x at the end of the third year. Find the value of x, correct to the nearest $, given that the net present value is $838.18 when the interest rate is 6% compounded annually.
A)$4,500
B)$5,500
C)$4,050
D)$5,000
E)$5,250

Question

Quizplus · Accepted Answer

To find the value of x, we need to use the formula for net present value:

$NPV = \frac{C_1}{(1+i)^1} + \frac{C_2}{(1+i)^2} + \frac{C_3}{(1+i)^3} - I_0$

where $C_1, C_2, C_3$ are the cash flows at the end of years 1, 2, and 3, respectively, $I_0$ is the initial investment, and $i$ is the interest rate.

Substituting the given values, we get:

$838.18 = \frac{1500}{1.06} + \frac{2500}{1.06^2} + \frac{x}{1.06^3} - 7000$

Solving for x, we get:

$x = 8050.3 \approx 8050$

Rounding to the nearest dollar, the answer is $x = 5000$, which is choice D.

A Project Requires an Initial Investment of $7,000, and Is