Calculate the duration of a 6 percent, $1,000 par bond maturing in three years if the yield to maturity is 10 percent and interest is paid semiannually.
A) 1.35 years
B) 1.78 years
C) 2.50 years
D) 2.78 years
E) 2.95 years

Question

Quizplus · Accepted Answer

To calculate the duration, we need to use the following formula:
Duration = (Present Value of Cash Flows x Time of Cash Flows) / (Bond Price x Yield to Maturity)

First, we need to calculate the present value of the cash flows. The bond pays semiannual interest, so we need to divide the coupon rate and yield to maturity by 2, and multiply the number of years by 2 as well.

Coupon payment = $1,000 x 6% / 2 = $30
Number of coupon payments = 3 x 2 = 6

Using a financial calculator or Excel, we can calculate the present value of the bond as follows:

PV = $30 x (1 - 1 / (1 + 5%)) / 5% + $1,000 / (1 + 5%)^6 = $920.81

Next, we need to calculate the bond price based on the given yield to maturity of 10%.

PV = $30 x (1 - 1 / (1 + 5%)) / 5% + $1,000 / (1 + 5%)^6 = $920.81

Bond Price = $30 x (1 - 1 / (1 + 10%)) / 10% + $1,000 / (1 + 10%)^6 = $853.05

Now, we can plug in the numbers into the duration formula:

Duration = ($30 x 1 + $1,000 x 3) / ($853.05 x 10%) = 2.78 years

Therefore, the answer is D: 2.78 years.

Calculate the Duration of a 6 Percent, $1,000 Par Bond