Answer:
2.2% change in the price of this bond if the market yield to maturity rises to 5.7 percent from the current rate of 5.5 percent.
Explanation:
Face Value = $1,000
Coupon payment = 1000 x 4.5% = $45 annually
Number of periods = n = 16 years
Price of bond is the present value of future cash flows, to calculate Price of the bond use following formula
Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]
Yield to maturity = 5.7%
Price of the Bond = $45 x [ ( 1 - ( 1 + 5.7% )^-16 ) / 5.7% ] + [ $1,000 / ( 1 + 5.7% )^16 ]
Price of the Bond = $876.18
Yield to maturity = 5.5%
Price of the Bond = $45 x [ ( 1 - ( 1 + 5.5% )^-16 ) / 5.5% ] + [ $1,000 / ( 1 + 5.5% )^16 ]
Price of the Bond = $895.38
Percentage Change = ( $895.38 - $876.18 ) / $876.18 = 2.2%
2.2% modification in the price of this bond if the market yield to maturity rises to 5.7 percent from the current rate of 5.5 percent.
The Face Value is = $1,000
Then the Coupon payment is = 1000 x 4.5% = $45 annually
After that Number of periods = n is = 16 years
When the Price of bond is the present value of future cash flows, Then to calculate Price of the bond use following formula are:
Price of the Bond is = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]
Then Yield to maturity = 5.7%
The Price of the Bond is = $45 x [ ( 1 - ( 1 + 5.7% )^-16 ) / 5.7% ] + [ $1,000 / ( 1 + 5.7% )^16 ]
The Price of the Bond is = $876.18
Then Yield to maturity is = 5.5%
After that Price of the Bond is = $45 x [ ( 1 - ( 1 + 5.5% )^-16 ) / 5.5% ] + [ $1,000 / ( 1 + 5.5% )^16 ]
Then Price of the Bond = $895.38
Therefore, the Percentage Change is = ( $895.38 - $876.18 ) / $876.18 = 2.2%
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