Use the table for the question(s)below.
Suppose the term structure of interest rates is shown below:

-Consider an investment that pays $1 000 at the end of each of the next four years. If the investment costs $3 500 and has a net present value (NPV)of $74.26, then the four-year risk-free interest rate is closest to:
A)4.53%
B)4.55%
C)4.5%
D)4.58%

Question

Use the table for the question(s)below.
Suppose the term structure of interest rates is shown below:
 
-Consider an investment that pays $1 000 at the end of each of the next four years. If the investment costs $3 500 and has a net present value (NPV)of $74.26, then the four-year risk-free interest rate is closest to:
A)4.53% 
B)4.55% 
C)4.5% 
D)4.58%

Quizplus · Accepted Answer

The NPV of an investment is calculated using the formula: NPV = ∑ (Ct / (1 + r)^t) - initial investment, where Ct is the cash inflow at time t, r is the discount rate (or the interest rate in this case), and t is the time period. Given that the NPV is $74.26 and the initial investment is $3,500, we can set up the equation for the NPV of this investment as follows: $74.26 = ($1,000 / (1 + r)^1) + ($1,000 / (1 + r)^2) + ($1,000 / (1 + r)^3) + ($1,000 / (1 + r)^4) - $3,500. Solving this equation for r requires trial and error or financial calculator/computer software. The correct interest rate that makes the NPV equal to $74.26 is approximately 4.53%.

Use the Table for the Question(s)below