Final answer:
The modified duration of the bond can be calculated using the Macaulay Duration and the yield to maturity. The Macaulay Duration is the weighted average number of years until the bond's cash flows are received. The modified duration is the Macaulay Duration divided by 1 plus the yield to maturity.
The correct answer is option c. 3.36
Step-by-step explanation:
The modified duration of the bond can be calculated using the following formula:
Modified Duration = Macaulay Duration / (1 + Yield to Maturity)
First, we need to calculate the Macaulay Duration. The Macaulay Duration is the weighted average number of years until the bond's cash flows are received, with the weight of each cash flow being its present value.
In this case, since the bond pays annual interest, the Macaulay Duration can be calculated as follows:
Macaulay Duration = [(1 x Present Value of the First Cash Flow) + (2 x Present Value of the Second Cash Flow) + ... + (n x Present Value of the Last Cash Flow)] / Bond Price
Since the bond matures in 4 years and its value at maturity is $1,000, the Macaulay Duration can be calculated as:
Macaulay Duration = [(1 x Present Value of $90) + (2 x Present Value of $90) + (3 x Present Value of $90) + (4 x Present Value of $1,090)] / $964
Next, we can use the Macaulay Duration and the yield to maturity of 6% to calculate the modified duration:
Modified Duration = Macaulay Duration / (1 + Yield to Maturity) = Macaulay Duration / (1 + 0.06)
Calculating the values:
Macaulay Duration = 3.56 years
Modified Duration = 3.56 / 1.06 ≈ 3.36 years
Therefore, the modified duration of this bond is approximately 3.36 years.