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What is the approximate modified duration of a 22-year bond, making semiannual coupon payments, with a...

What is the approximate modified duration of a 22-year bond, making semiannual coupon payments, with a coupon rate of 5% and a current price of 69.18 per 100 of par value, considering a 50 bps change in discount rate?

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Expert Solution

Par Value $                    100.00
Nper 44
Coupon (semi annual) $                         2.50
Coupon Rate 5%
Coupon per year 2
Years to maturity 22
Current Price $                       69.18
Yield to maturity (YTM) 8.0%
Formula Explained
Nper Total number of payment periods
Coupon per year * years of maturity
PMT Interest Payments, Par value*Coupon rate divided by coupons per year
PV The current price of the bond, which is negative because it’s the cost to buy today
FV Par value, because this is the future value of the bond at maturity
Type 0, default
Re annualizing Coupon per year
Price when YTM changes 50 bps change in the discount factor
YTM 1 8.50%
YTM 2 7.50%
Price of bond for YTM 1 $65.42
Price of bond for YTM 2 $73.26
Modified Duration 11.33948121

Formula for Modified Duration		 (Price of bond with YTM 2 -Price of bond with YTM 1) divided by (2* Initial price* change in yield)

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jeff jeffy answered 2 years ago
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