Question

A 10-year bond with face value of $1,000 has a couple rate of 6% paid semiannually. If the bond is purchased for $1,251.26, what is the yield to maturity rate of interest per year would be realized on this investment opportunity? Use interpolation method to find i'.

Answer 1

The price of bond is computed using the rule

Price of bond = present worth of coupon payment + present worth of face value

1251.26 = 30(P/A, i%, 20) + 1000(P/F, i%, 20)

Now this becomes

-1251.26 + 30(P/A, i%, 20) + 1000(P/F, i%, 20) = NPV = 0

For i = 1%, NPV is 109.65 and for i = 1.5% NPV is 6.27. For i = 1.6%, NPV is -13.25

Hence the required i = 1.5% + (1.6% - 1.5%)*(6.27/(6.27 + 13.25)) = 1.532% per semi annual period

The yield to maturity rate of interest per year is (1 + 1.532%)^2 - 1 = 3.087%