Response: We Use a Present Value Table to Look

Response: We use a present value table to look up the value of the $1000 principal to be paid 8 years or 16 semi-annual periods. Looking at the 3% row (rate per semi-annual period) , we find the factor of .623. Multiplying by $1000, the investor is selling the value of the principal for $623.00. Using a present value of an annuity table, we also look up R=3% and N=16 to find the factor 12.561. Multiplying 12.561 times the $40 semi-annual coupon, we find our investor is selling the remaining stream of 16 coupon payments for $502.44. Thus the price of the bond is $623.00 + $502.44 = $1,125.44. But the bond originally cost our investor $1,000, so the capital gain is 125.44 (using financial calculator, the answer is $125.61) . Section: Measuring Bond Yields.
-Examine Example 17-13. The basic data is repeated here, in financial calculator format: FV = 1000, N=30, PMT=50 $\begin{array}{|l|l|l|}\hline \text { I/Y } & \text { Price=PV } & \% \text { change } \\\hline \text { At } 10 \% & \$ 1,000.00 & \\\hline \text { At } 8 \% & \$ 1,172.93 & +17.29 \% \\\hline \text { At } 12 \% & \$ 862.35 & -13.77 \% \\\hline\end{array}$
Why are the % changes different?

A) They are actually the same: the table includes an error.
B) The prices shown are rounded to the nearest penny, slightly moving the % changes.
C) The relationship between interest rates and price is not linear.
D) Other factors, including duration and coupon rate, will also affect the relationship between interest rates and prices.