Face Value of bond = $1000
Annual Coupon Payment = $1000*8%
= $80
No of years to maturity(n) = 3 years
When the Market Interest rate was 8%, the Price of the bond will be the same as the Par value which is $1000 because when the Coupon rate and Market Interest rate are the same the Bond sells at par Value.
So, At an 8% Interest rate price is $1000
- Interest rate(YTM) changed to 8.86%
Calculating the Price of Bond:-
Price = \frac{CouponPayment}{(1+YTM)^{1}}+\frac{CouponPayment}{(1+YTM)^{2}}+...+\frac{CouponPayment}{(1+YTM)^{n}}+\frac{FaceValue}{(1+YTM)^{n}}
Price = \frac{80}{(1+0.0886)^{1}}+\frac{80}{(1+0.0886)^{2}}+\frac{80}{(1+0.0886)^{3}}+\frac{1000}{(1+0.0886)^{3}}
Price =$203.008 + $775.166
Price = $978.17
So, when the Interest rate changed to 8.86% the price falls to $978.17
Change in Price due to increase in Interest rate = $978.17 - $1000
= -$21.83
Hence, the price decreased by $21.83
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