You have discovered that when the required rate of return on a bond you own fell by 0.5 percent from 8.2 percent to 7.7 percent, the fair present value rose from $950 to $970. The bond pays interest annually. What is the duration of this bond? Assume annual payments.

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Business

Carl Webb

31 March, 06:25

You have discovered that when the required rate of return on a bond you own fell by 0.5 percent from 8.2 percent to 7.7 percent, the fair present value rose from $950 to $970. The bond pays interest annually. What is the duration of this bond? Assume annual payments.

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Terry Houston · Answer 1

4.5 years

Explanation:

the change in price = $970 - $950 = $20

the change in rate of return = 7.7% - 8.2% = - 0.5% or - 0.005

to determine the duration of the bond we can use the following formula:

duration = (Δ price / price) / [Δ rate / (1 + rate) ]

= ($20 / $970) / [-0.005 / (1 + 0.077) ] = 0.0206 / (-0.0046) = - 4.48 years ≈ 4.5 years (remaining time is positive)