Question

What is the duration of a 5-year par value zero coupon bond yielding 10 percent annually? 1) 0.50 years 2) 2.00 years 3) 4.40 years 4) 5.00 years 5) 4.05 years

Answer 1

The duration of a 5-year par value zero coupon bond yielding 10 percent annually is 4) 5.00 years.

Step-by-step explanation:

The duration of a bond is a measure of its sensitivity to changes in interest rates. It represents the weighted average time it takes to receive the bond's cash flows.

In this case, we have a 5-year par value zero coupon bond yielding 10 percent annually. Since it is a zero coupon bond, there are no periodic coupon payments. The cash flow is only received at the end of the 5-year maturity period.

To calculate the duration of the bond, we can use the formula:

Duration = (Present Value of Cash Flow * Time Period) / Total Present Value

In this case, the bond has a par value of $1,000 and a yield of 10 percent annually. The present value of the cash flow can be calculated as:

Present Value = Par Value / (1 + Yield)^Time Period

Using these formulas, we can calculate the duration of the bond as follows:

Calculate the present value: Present Value = $1,000 / (1 + 0.10)^5 = $620.92

Calculate the weighted average time: Weighted Average Time = (Present Value * Time Period) / Total Present Value = ($620.92 * 5) / $620.92 = 5 years

Therefore, the duration of a 5-year par value zero coupon bond yielding 10 percent annually is 4) 5.00 years.