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The present value (price) formula for a coupon bond is:
PV = C/(1+i) + C/(1+i)2 + ... + C/(1+i)n + F/(1+i)n
Part a
The present value (price) formula for a zero coupon bond is:
PV = F/(1+i)n
Plugging in the given information,
Price = $1000/(1+0.1)15 = $239.39
Thus the price of the fifteen-yr zero coupon bond is $239.39.
Part b
Semiannual coupon = 6%*$500/2 = $15
Price = $15/(1+(0.1/2)) + $15/(1+(0.1/2))2 +..... + $15/(1+(0.1/2)6 + $500/(1+(0.1/2)6 = $449.24
Thus the price of the three-yr semiannual 6% coupon bond is $449.24.
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It is a numerical average, as equal to the sum of terms in a given series divided by the number of terms in that series is the mean which is also called the expected value.
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