Price of the bond could be calculated using below formula.
P = C* [{1 - (1 + YTM) ^ -n}/ (YTM)] + [F/ (1 + YTM) ^ -n]
Where,
Face value = $1000
Coupon rate = 7%
YTM or Required rate = 6%
Time to maturity (n) = 15 years
Annual coupon C = $70
Let's put all the values in the formula to find the bond current value
P = 70* [{1 - (1 + 0.06) ^ -15}/ (0.06)] + [1000/ (1 + 0.06) ^15]
P = 70* [{1 - (1.06) ^ -15}/ (0.06)] + [1000/ (1.06) ^15]
P = 70* [{1 - 0.41727}/ 0.06] + [1000/ 2.39656]
P = 70* [0.58273/ 0.06] + [417.26475]
P = 70* 9.71217 + 417.26475
P = 679.8519 + 417.26475
P = 1097.11665
So price of the bond is $1097.12
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When the market rate changes to 9% bond price will be
Face value = $1000
Coupon rate = 7%
YTM or Required rate = 9%
Time to maturity (n) = 15 years
Annual coupon C = $70
Let's put all the values in the formula to find the bond current value
P = 70* [{1 - (1 + 0.09) ^ -15}/ (0.09)] + [1000/ (1 + 0.09) ^15]
P = 70* [{1 - (1.09) ^ -15}/ (0.09)] + [1000/ (1.09) ^15]
P = 70* [{1 - 0.27454}/ 0.09] + [1000/ 3.64248]
P = 70* [0.72546/ 0.09] + [274.53823]
P = 70* 8.06067 + 274.53823
P = 564.2469 + 274.53823
P = 838.78513
So price of the bond is $838.79
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Change in price = 1097.12 - 838.79 = 258.33
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