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An investor wants to find the duration of​ a(n) 25​-year, 10​% semiannual​ pay, noncallable bond​ that's...

An investor wants to find the duration of​ a(n) 25​-year, 10​% semiannual​ pay, noncallable bond​ that's currently priced in the market at ​$ 842.38​, to yield 12​%. Using a 100 basis point change in​ yield, find the effective duration of this bond ​.

The new price of the bond if the market interest rate decreases by 100 basis points​ (or 1​%) is ​$______

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6.50% Period (p) Rt p *cf present value 50.00 $ 50.00$ 50.00 100.00 $ 50.00 $ 150.00 $ 50.00 $ 200.00 $ 50.00 $ 250.00 $ 50.00 $ 300.00 $ 50.00 $ 350.00 $ 50.00 $ 400.00 $ 50.00 $ 450.00 $ 50.00 $ 500.00 $ 50.00 $ 550.00 $ 50.00 $ 600.00 $ 50.00 $ 700.00 $ 50.00 $ 750.00 $ 50.00 $ 2,450.00 $ 50$ 1,050.00 $52,500.00 $ Yield Yield Face value 11.0% annual 47.17 89.00 125.94 158.42 186.81 211.49 232.77 250.96 266.35 279.20 289.73 298.18 309.61 312.95 140.99 2,850.14 1 6.0% semi annual 1,000.00 4 10.0% annual Coupon Coupon 5.0% semi annual Coupon payment 50.00 10 $ 11 $ 12 $ 14 15 $ 49 Time 25.00 Number of payments 50.00 Total 14,375 Duration = Total Value / Face Value Duration 14.38

Please note that there are 50 payments and it is difficult to put screen shot of that. I think this will give you fair idea how to solve for duration

Present value = payment / ( 1+ semi annual yield ) ^ n

Since duration is 14.38

It means that 1% change in interest rate will lead to 14.38% change in price of bond

So 1% decrease in rates will increase the price by 14.38%

So

New price = 842.38 * 1.1438 = 963.514


answered by: ANURANJAN SARSAM
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