A par value bond offers a coupon rate of 7 percent with semi

A par value bond offers a coupon rate of 7 percent with semiannual interest payments. The effective annual rate provided by these bonds must be:

equal to 3.5 percent

greater than 3.5 percent but less than 4 percent

equal to 7 percent

greater than 7 percent but less than 8 percent

equal to 14 percent

Solution

Answer is greater than 7% but less than 8%

Based on the relationship between YTM and coupon rate,

If YTM > Coupon Rate, price of bond is greater than par value.

If YTM < Coupon Rate, price of bond is lower than par value.

If YTM = Coupon Rate, price of bond is equal to par value.

Now, in question, bond is a par value bond, which means YTM = Coupon rate. There fore for that bond, YTM = 7%.

Semi-annual YTM = 7%/2 = 3.5%

Semi-annual rate = 3.5%--> we need to convert it to effective annual rate

Effective annual rate = (1 + 3.5%)² - 1 {power of 2 means 2 semi-annual periods per year)

=> Effective annual rate = 1.071225 - 1 = 0.071225

=> Effective annual rate = 7.1225%. Clearly option D matches to the outcome.