Compute the duration of an 8%, 5-year corporate bond with a par value of $1000 if yield to maturity is 10%.

Question

Quizplus · Accepted Answer

The formula for calculating duration is: 
Duration = (Present value of cash flows x time period)/ Bond price x Yield to maturity

The present value of cash flows is calculated using the following formula:
PV = C1/(1 + r) + C2/(1 + r)² + ... Cn/(1 + r)^n
where C1, C2, ..., Cn are the cash flows and r is the yield to maturity.

For a 5-year corporate bond with a 8% coupon rate and a $1000 par value, the cash flows will be $80 per year for 5 years.
Using the formula for calculating present value:
PV = 80/(1 + 0.10) + 80/(1 + 0.10)² + ... + 1080/(1 + 0.10)^5
PV = $326.95

Using the formula for calculating duration:
Duration = ($326.95 x 5)/$1000 x 0.10
Duration = 1.63475

Therefore, the duration of the bond is 4.28 years (rounded to two decimal places).

Compute the Duration of an 8%, 5-Year Corporate Bond with a Par