The duration of a five-year bond with 7% annual coupons and a yield-to-maturity of 8% is closest to:

Question

Quizplus · Accepted Answer

To calculate the duration of a bond, we need to take into account the timing of the cash flows and the present value of each cash flow. The formula for duration is:

Duration = (Present value of cash flow * time of cash flow) / Bond price

For this bond, the cash flows are 7% of the face value ($1000) each year for 5 years, plus the face value at maturity. The present value of each cash flow is calculated using the yield-to-maturity of 8%.

Using a financial calculator, we can find the present value of the bond to be $943.70.

The duration of the bond is calculated as follows:

Duration = [(70 / 1.08) * 1 + (70 / 1.08^2) * 2 + (70 / 1.08^3) * 3 + (70 / 1.08^4) * 4 + (1070 / 1.08^5) * 5] / $943.70

Duration = 4.4 years

Therefore, the closest answer choice is C) 4.4 years.

The Duration of a Five-Year Bond with 7% Annual Coupons