Suppose a ten-year, $ 1000 bond with an 8.2 % coupon rate and semiannual coupons is trading for $ 1 035.55.
a. What is the bond's yield to maturity (expressed as an APR with semiannual compounding)?
b. If the bond's yield to maturity changes to 9.6 % APR, what will be the bond's price?
(please show all work)!
a)
Coupon = (8.2% of 1000) / 2 = 41
Number of periods = 10 * 2 = 20
Bond's yield to maturity = 7.68%
Keys to use in a fianncial calculator:
2nd P/Y 2
FV 1000
PV - 1035.55
PMT 41
N 20
CPT I/Y
b)
Rate = 9.6% / 2 = 4.8%
Bond's price = Coupon * [1 - 1 / (1 +r)n] / r + FV / (1 + r)n
Bond's price = 41 * [1 - 1 / (1 +0.048)20] / 0.048 + 1000 / (1 + 0.048)20
Bond's price = 41 * [1 - 0.391538] / 0.048 + 391.538387
Bond's price = 41 * 12.676292 + 391.538387
Bond's price = $911.27
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