Calvin and Andre both have bonds they bought at par value which pay a 10.25% coupon rate. Calvin's bond has 10 years to maturity and Andre's bond has 20 years to maturity. If interest rates suddenly rise to 12.25%, what is the approximate change in value of Calvin's bond?
Multiple Choice
-14.81%
14.81%
11.35%
-11.35%
Given about Calvin's bond,
Face value = $1000
Since bond is priced at par, its price = face value
=> price of the bond = $1000
coupon rate = 10.25% paid semiannually,
So, semiannual coupon = (10.25%/2) of 1000 = $51.25
years to maturity = 10 years
If YTM suddenly increased to 12.25%, new price of the bond can be calculated using financial calculator with following values:
FV = 1000
N = 10*2 = 20
PMT = 51.25
I/Y = 12.25/2 = 6.125
Solve for PV, we get PV = -886.46
So, new price of the bond = 886.46
Change in price = (new price - old price)/old price = (886.46 - 1000)/1000 = -11.35%
Option D is correct.
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